Six boxes -  P, Q, R, S, T and U.

1) Only two boxes are placed between box S and U. 

2. Box R is immediately above box U. 

3) Box S is neither placed at the top nor at the bottom. 

4) Box Q is immediately below box S.

<br>

5)  More than two boxes are placed below box T. 

6) Box P is placed below box T and box T is not at the Top.

This will eliminate case 2 and case 3.

Therefore, the final arrangement is as:

<br>

Hence, box U is immediately above box T.

Six boxes -  P, Q, R, S, T and U.

1) Only two boxes are placed between box S and U. 

2. Box R is immediately above box U. 

3) Box S is neither placed at the top nor at the bottom. 

4) Box Q is immediately below box S.

<br>

5)  More than two boxes are placed below box T. 

6) Box P is placed below box T and box T is not at the Top.

This will eliminate case 2 and case 3.

Therefore, the final arrangement is as:

<br>

Checking each option:

Option 1:  Only two boxes are placed between U and P. → False.

Option 2: Box T is paced exactly between box R and P. → False.

Option 3: Box S is immediately below box P. → True.

Option 4: Number of boxes above box U is same as number of boxes below P. → False.

Option 5: Box R is immediately below box T. → False.

Hence, option (3) is true.

Six boxes -  P, Q, R, S, T and U.

1) Only two boxes are placed between box S and U. 

2. Box R is immediately above box U. 

3) Box S is neither placed at the top nor at the bottom. 

4) Box Q is immediately below box S.

<br>

5)  More than two boxes are placed below box T. 

6) Box P is placed below box T and box T is not at the Top.

This will eliminate case 2 and case 3.

Therefore, the final arrangement is as:

<br>

Hence, 3 boxes are placed between box R and S.

Six boxes -  P, Q, R, S, T and U.

1) Only two boxes are placed between box S and U. 

2. Box R is immediately above box U. 

3) Box S is neither placed at the top nor at the bottom. 

4) Box Q is immediately below box S.

<br>

5)  More than two boxes are placed below box T. 

6) Box P is placed below box T and box T is not at the Top.

This will eliminate case 2 and case 3.

Therefore, the final arrangement is as:

<br>

All the given options (R - U, T - P, P - S, and S - Q) except option (P - Q) are immediate boxes to each other.

Hence, P - Q is different from the other.

Six boxes -  P, Q, R, S, T and U.

1) Only two boxes are placed between box S and U.

2. Box R is immediately above box U. 

3) Box S is neither placed at the top nor at the bottom. 

4) Box Q is immediately below box S.

<br>

5)  More than two boxes are placed below box T. 

6) Box P is placed below box T and box T is not at the Top.

This will eliminate case 2 and case 3.

Therefore, the final arrangement is as:

<br>

Hence, box R is placed at the top.

The pattern for the code is as follows:

Similarly,

Hence, 'PURPLE' is coded as 'RYXVPG'.

Given: A certain number of persons are sitting in a row facing north

1. H sits at the extreme left end of the row

2. Two persons sit between H and N
   

<br>

3) Only six people sit to the left of G.

4. Two persons sit between G and S, who sits fourth to the right of R
   

<br>

5. The number of persons sitting between N and G is the same as the number of persons sitting between S and the one who is sitting at the extreme right end of the row.
   

<br>

Hence, G is sitting immediate right of R.

Given: A certain number of persons are sitting in a row facing north

1. H sits at the extreme left end of the row

2. Two persons sit between H and N
   

<br>

3) Only six people sit to the left of G.

4. Two persons sit between G and S, who sits fourth to the right of R
   

<br>

5. The number of persons sitting between N and G is the same as the number of persons sitting between S and the one who is sitting at the extreme right end of the row.
   

<br>

Hence, 13 persons are sitting in a row.

Given: A certain number of persons are sitting in a row facing north

1. H sits at the extreme left end of the row

2. Two persons sit between H and N
   

<br>

3) Only six people sit to the left of G.

4. Two persons sit between G and S, who sits fourth to the right of R
   

<br>

5. The number of persons sitting between N and G is the same as the number of persons sitting between S and the one who is sitting at the extreme right end of the row.
   

<br>

Hence, R is sitting between N and G.

Given: A certain number of persons are sitting in a row facing north

1. H sits at the extreme left end of the row

2. Two persons sit between H and N
   

<br>

3) Only six people sit to the left of G.

4. Two persons sit between G and S, who sits fourth to the right of R
   

<br>

5. The number of persons sitting between N and G is the same as the number of persons sitting between S and the one who is sitting at the extreme right end of the row.
   

<br>

Hence, N is sitting sixth to the left of S.

Given: A certain number of persons are sitting in a row facing north

1. H sits at the extreme left end of the row

2. Two persons sit between H and N
   

<br>

3) Only six people sit to the left of G.

4. Two persons sit between G and S, who sits fourth to the right of R
   

<br>

5. The number of persons sitting between N and G is the same as the number of persons sitting between S and the one who is sitting at the extreme right end of the row.
   

<br>

Hence, 3 persons are sitting between R and S**.**

1. P's birthday is in January.

2. There are the same number of person having their birthday before and after R. ‘

3. Only one person's birthday is there between S and R.

4. Q's birthday is in the month having 31 days but not in August.

5. There are two person's birthday between Q and V.  

6. T's birthday is before U's birthday

 

7. Q's birthday is not before R.  (This eliminates case 2)

 

Hence, S's birthday is in march.

1. P's birthday is in January.

2. There are the same number of person having their birthday before and after R. ‘

3. Only one person's birthday is there between S and R.

4. Q's birthday is in the month having 31 days but not in August.

5. There are two person's birthday between Q and V.  

6. T's birthday is before U's birthday

 

7. Q's birthday is not before R.  (This eliminates case 2)

 

Hence, T's birthday is in June.

1. P's birthday is in January.

2. There are the same number of person having their birthday before and after R. ‘

3. Only one person's birthday is there between S and R.

4. Q's birthday is in the month having 31 days but not in August.

5. There are two person's birthday between Q and V.  

6. T's birthday is before U's birthday

 

7. Q's birthday is not before R.  (This eliminates case 2)

 

Five persons have their birthday before Q.

Hence, More than four is the correct answer.

1. P's birthday is in January.

2. There are the same number of person having their birthday before and after R. ‘

3. Only one person's birthday is there between S and R.

4. Q's birthday is in the month having 31 days but not in August.

5. There are two person's birthday between Q and V.  

6. T's birthday is before U's birthday

 

7. Q's birthday is not before R.  (This eliminates case 2)

 

All of them having birthday in the month which has 31 days except T

Hence, T is odd one out.

1. P's birthday is in January.

2. There are the same number of person having their birthday before and after R. ‘

3. Only one person's birthday is there between S and R.

4. Q's birthday is in the month having 31 days but not in August.

5. There are two person's birthday between Q and V.  

6. T's birthday is before U's birthday

 

7. Q's birthday is not before R.  (This eliminates case 2)

Hence, U has his birthday at last.

As per the given information,

1. Point A is 8m south of point F.

2. Point B is 5m east of point H,

3. H is 4m north of point E.

4. Point G is 15m west of point D,

5. D is 9m south of point B.

6. Point C is 7m south of point G.

7. Point A is 5m west of point E.

Therefore the final arrangement is, 

 Hence, South West is the direction of Point C with respect to Point F

As per the given information,

1. Point A is 8m south of point F.

2. Point B is 5m east of point H,

3. H is 4m north of point E.

4. Point G is 15m west of point D,

5. D is 9m south of point B.

6. Point C is 7m south of point G.

7. Point A is 5m west of point E.

Therefore the final arrangement is, 

 the total distance between  F and B is

= 8 + 5 + 4 + 5

= 22 m

 Hence, 22m is the total distance between  F and B.

As per the given information,

1. Point A is 8m south of point F.

2. Point B is 5m east of point H,

3. H is 4m north of point E.

4. Point G is 15m west of point D,

5. D is 9m south of point B.

6. Point C is 7m south of point G.

7. Point A is 5m west of point E.

Therefore the final arrangement is, 

As per the question, 

Hence, 5m is the distance between Pont Y and Point H.

Statement: J ≤ K < T = A ≥ W = C

i) W = T ⇒ False (as T = A ≥ W ⇒ T ≥ W thus the relation between W and T cannot be established)

ii) T > W ⇒ False (as T = A ≥ W ⇒ T ≥ W thus the relation between W and T cannot be established) 

So, T ≥ W means either T > W or T = W

Hence, either I or II is true.

Statement: C = B < F ≤ H > R = D ≥ K

i) F > D ⇒ False (as F ≤ H > R = D, thus relation between F and H cannot be determined)

ii) R > B ⇒ False (as B < F ≤ H > R, thus relation between R and B cannot be determined)

Hence, neither I nor II is true.

Statement: E > T ≥ F > Z = V < I ≤ R

i) V < T ⇒ True (as T ≥ F > Z = V ⇒ T > V or V < T)

ii) R > Z ⇒ True (as Z = V < I ≤ R ⇒ Z < R or R > Z) 

Hence, both I and II are true.

The least possible Venn diagram for the given statements is as follows,

      

Conclusion:

I. All teacher are employee → False (it is possible but not definite)

II. Some employee are boss → True (as all boss are employee)

Hence, only conclusion II follows.

The least possible Venn diagram for the given statements is as follows,

Conclusions:

I. All Dentists are Teachers → False (as All the teacher is Dentist, Some part of Dentist not Teacher. So, it is false) 

II. All teachers are Dentists  → True (All Teacher is Professor and All Professor are Dentist 

hence all teachers are dentists ) 

 Hence, only II follows.

The least possible Venn diagram for the given statements is as follows

Conclusions:

I. Some Houses are Room → True (As we can see, all Rooms are House. So, some Houses are Room is true.)

II. No Room is Flat → True (As we can see, all Rooms are House and no House is Flat. So, no Room is Flat is true.)

Hence, both I and II follow.

Given series is: (Left) H M @ L 1 9 A 3 X & 8 W 5 ! F C V # % N K 7 2 Z a Q B G € µ T (Right)

Arrangement required: Consonant → Number

(Left)   H M @ L 1 9 A 3 X & 8 W 5 ! F C V # % N K 7 2 Z a Q B G € µ T       (Right)

Hence, three such pairs are there i.e. L1, W5, K7

Given series is: (Left) H M @ L 1 9 A 3 X & 8 W 5 ! F C V # % N K 7 2 Z a Q B G € µ T (Right)

19^th element from right end is ‘5’

and 21^st element from the left end is ‘K’.

Given series is: (Left) H M @ L 1 9 A 3 X & 8 W 5 ! F C V # % N K 7 2 Z a Q B G € µ T (Right)

Clearly, there are 7 elements between  the19^th element from the right and the 21^st element from the left end of the arrangement: !, F, C, V, #, %, N

Hence, seven is the correct answer.

Given series is: (Left) H M @ L 1 9 A 3 X & 8 W 5 ! F C V # % N K 7 2 Z a Q B G € µ T (Right)

Arrangement required: Letter → Symbol → Letter

Left side: H M @ L 1 9 A 3 X & 8 W 5 ! F C V # % N K 7 2 Z a Q B G € µ T : Right side

Hence, only one such pair is there i.e. M@L.

Given series is: (Left) H M @ L 1 9 A 3 X & 8 W 5 ! F C V # % N K 7 2 Z a Q B G € µ T (Right)

Left + Right = Left

15^th from the left + 6^th to the right = 21^st from the left

(Left) H M @ L 1 9 A 3 X & 8 W 5 ! F C V # % N K 7 2 Z a Q B G € µ T (Right)

Clearly, 21^st from the left is ‘K’.

Hence, K is the correct answer.

Given series: 821 497 133 986 577

On interchanging first and last digit,

821 → 128

497 → 794

133 → 331

986 → 689

577 → 775

Arranging in increasing order: 128 331 689 775 794

Hence, “775” is the second highest number.

Hence, 577 is the correct answer.

Given series: 821 497 133 986 577

Subtracting 1 from second digit and adding 1 to the last digit:

812 488 124 977 568

Hence, “977” is the only number which is not divisible by 4.

Given series: 821 497 133 986 577

In each number three digits arranged in descending order

New series obtained:  821 974 331 986 775

Hence, “775” is second lowest number.

The pattern followed here is :

1. JB

J (10) + B (2) = 12

2. DH

D (4) + H (8) = 12

3. KA

K (11) + A(1) = 12

4. EJ

E (5) + J (10) = 15

Resultant of all options is “12” except “EJ”

Hence, ‘EJ’ is odd among them.

As per the given information,

1. D sits at the corner of the table. G sits second to the right of D. Only two people sit between G and B.

2. C is one of the immediate neighbors of B. H sits second to the left of C.

3. E sits second to the left of F. G is not an immediate neighbor of F. As no proper place of E, Hence case-2 ruled out.

Therefore, the final arrangement will be, 

 

All, except H, are facing outside the center.

H is the odd one out.

As per the given information,

1. D sits at the corner of the table. G sits second to the right of D. Only two people sit between G and B.

2. C is one of the immediate neighbors of B. H sits second to the left of C.

3. E sits second to the left of F. G is not an immediate neighbor of F. As no proper place of E, Hence case-2 ruled out.

Therefore, the final arrangement will be, 

 

A sits in the middle of H and G is the correct answer.

As per the given information,

1. D sits at the corner of the table. G sits second to the right of D. Only two people sit between G and B.

2. C is one of the immediate neighbors of B. H sits second to the left of C.

3. E sits second to the left of F. G is not an immediate neighbor of F. As no proper place of E, Hence case-2 ruled out.

Therefore, the final arrangement will be, 

Four persons sit between C and A, when counted from the right of C.

As per the given information,

1. D sits at the corner of the table. G sits second to the right of D. Only two people sit between G and B.

2. C is one of the immediate neighbors of B. H sits second to the left of C.

3. E sits second to the left of F. G is not an immediate neighbour of F. As no proper place of E, Hence case-2 ruled out.

Therefore, the final arrangement will be, 

 

B sits second to the right of F.

As per the given information,

1. D sits at the corner of the table. G sits second to the right of D. Only two people sit between G and B.

2. C is one of the immediate neighbors of B. H sits second to the left of C.

3. E sits second to the left of F. G is not an immediate neighbor of F. As no proper place of E, Hence case-2 ruled out.

Therefore, the final arrangement will be, 

 

D sits third right of A.

The given word is represented as follow,

Hence we got two pairs- EI and RT.

Hence, “None of the above” is the correct answer.

<br>

Hence, 'Y' is the correct answer.

Given:

Time taken by Niya alone to complete the work = 10 days

Time taken by Niya and Kriya to complete the work = 6 Days

Riya = 20% more efficient then kriya

Formula used:

(1/t) = (1/t₁) + (1/t₂)

Where, t = time taken to complete whole work,

t₁ and t₂ = time taken by 1 and 2 to complete work alone

Efficiency = (Total work)/(Time taken)

Calculation:

Let time taken by Kriya be x days.

⇒ (1/6) = (1/10) + (1/x)

⇒ (1/x) = (1/6) - (1/10)  (5 - 3)/30 

⇒ (1/x) = (5 - 3)/30

⇒ (1/x) = 2/30

⇒ x = 30/2 

⇒ x = 15

Time taken by Kriya = 15 days.

If Riya is 20% more efficient than kriya

So, time to complete the work by Riya = 15/{(100 + 20)/100} 

⇒ 1500/120

⇒ 12.5 days

∴ Riya alone can complete the work in 12.5 days.

Alternate Method Let total work = 30

Efficiency of Niya = 3 

Then efficiency of Kriya = 5 - 3 = 2

Riya is 20% more efficient then kriya then

Efficiency of kriya = 1.2 × 2 = 2.4

Riya complete work when working alone = 30/2.4 = 12.5 days.

Given:  

Shubham invests Rs.2250, and after some time Shivam invests Rs. 2500

Calculation: 

Let the time after which Shivam invest his rupees be x

⇒ Shubham's Profit = 6050 - 2750 = 3300 Rs.

⇒ Shivam's profit = 2750 Rs.

The ratio of the profit = 3300 : 2750

⇒  6 : 5

Because the ratio of the capital is equals to the ratio of the profit then,

⇒ 2250 × 12 : 2500 × x = 6 : 5

⇒ 5 ( 2250 × 12) = 6 ( 2500 × x)

⇒  x = 9 months

∴  Shivam invested after 3 months.

Let the cost price of an item be Rs.A.

Selling price of 8 items = Rs.12A

Selling price of an item = 12A/8 = Rs. 3A/2

Marked price of an item = Rs.1500

Selling price of an item = 1500 × 80/100 = Rs.1200

⇒ 3A/2 = 1200

⇒ A = Rs.800

The cost price of an item = Rs.800

Profit percentage = (1200 – 800)/800 × 100

∴ Profit percentage = 50%

Given:

156, 110, 72, 42, 20, ?

Calculation:

From the above series, the logic can be explained as:

13 × 12 = 156

11 × 10 = 110

9 × 8 = 72

7 × 6 = 42

5 × 4 = 20

3 × 2 = 6

∴ The required value of "?" is 6.

Alternate Method

Calculation:

The logic of the above series can be explained as below

∴ The required value of "?" is 6.

Given:

12, 16, 25, 41, 66, ? 

Calculation:

The series follows the following pattern

⇒ 12 + 22 = 16

⇒ 16 + 32 = 25

⇒ 25 + 42 = 41

⇒ 41 + 52 = 66

⇒ 66 + 62 = 102

∴ The required value of ? is 102

Given:

6, 6, 12, 36, 144, ?

Calculation:

The series follows the following pattern:

6 × 1 = 6

6 × 2 = 12

12 × 3 = 36

36 × 4 = 144

144 × 5 = 720

∴ 720 will come in place of the question mark ('?').

Given:

107, 222, 352, 512, ?, 1072

Calculation:

Pattern of the given series can be explained as:

∴ The value '?' is 732.

The correct answer is: 2

 

Given:

20, 33, 50, 69, 92, ?

Calculation:

the given series follows the following pattern:

20 + 13 = 33

33 + 17 = 50

50 + 19 = 69

69 + 23 = 92

92 + 29 = 121

here; 13 , 17 , 19 , 23 & 29 are prime numbers.

∴ 121 will come in place of ?

Given:

95 ÷ 19 + √49 – 27 ÷ 9 = √? 

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

95 ÷ 19 + √49 – 27 ÷ 9 = √? 

⇒ 5 + 7 – 3 = √?

⇒ 9 = √?

⇒ ? = 81

∴ The value of ? is 81.

Given:

840 ÷ 14 + 6 × 9 + ? = 187

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

840 ÷ 14 + 6 × 9 + ? = 187

⇒ 60 + 54 + ? = 187

⇒ 114 + ? = 187

⇒ ? = 187 - 114 = 73

∴ The value of ? is 73.

Given:  

200 ÷ 8 of 5 + 12.5 × 20 = 5 × ?

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

200 ÷ 8 of 5 + 12.5 × 20 = 5 × ?

⇒ 200 ÷ 40 + 12.5 × 20 = 5 × ?

⇒ (200/40) + 250 = 5 × ?

⇒ 5 + 250 = 5 × ?

⇒ 255 = 5 × ?

⇒ ? = 255/5

⇒ ? = 51

∴ 51 will come in place of the question mark ('?').

Given:

(2197)1/3 + 192 - 122 = ? - (60 × 5)

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

(2197)1/3 + 192 - 122 = ? - (60 × 5)

⇒ 13 + 361 - 144 = ? - 300

⇒ 374 - 144 = ? - 300

⇒ 230 + 300 = ?

⇒ ? = 530

∴ The value of ? is 530.

Given:

(25% of 900 + ? + 22 × 62)  = 28

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

(25% of 900 + ? + 22 × 62)  = 28²

⇒ [(1/4) × 900 + ? + 4 × 36) = 28²

⇒ (225 + ? + 144) = 28²

⇒ (225 + ? + 144) = 784

⇒ 369 + ? = 784

⇒ ? = 415

∴ The value of ? is 415.

Given:

40% of (2.5 × 4 + ?) = 24

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

40% of (2.5 × 4 + ?) = 24

⇒ 40% of (10 + ?) = 24

⇒ 4 + 0.4(?) = 24

⇒ 0.4(?) = 20

⇒ ? = 50

∴ The value of ? is 50.

Alternate Method

Calculation:

40% of (2.5 × 4 + ?) = 24

⇒ 40% of (10 + ?) = 24

⇒ (10 + ?) = 60

⇒ ? = 50

∴ The value of ? is 50.

Given:  

45% of 400 + 20% of ? = 25% of 40

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

45% of 400 + 20% of ? = 25% of 40

⇒ (45/100) × 400 + (20/100) × ? = (25/100) × 40

⇒ 45 × 4 + (?/5) = 40/4

⇒ 180 + (?/5) = 10

⇒ ?/5 = 10 - 180

⇒ ?/5 = -170

⇒ ? = -850

∴ -850 will come in place of the question mark ('?').

Given:

33.33% of 36 × ?% of 30 = 3600

Concept Used:

Calculation:

33.33% of 36 × ?% of 30 = 3600

⇒ 1/3 of 36 × ?% of 30 = 3600

⇒ 12 × ?% of 30 = 3600

⇒ ?% of 30 = 3600/12

⇒ ? = (300 × 100)/30

⇒ ? = 1000

∴ 1000 will come in place of the question mark ('?').

Additional Information

Given:

12.5 × 30 - √324 = ?2 - ∛64

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

12.5 × 30 - √324 = ?2 - ∛64

⇒ 375 - 18 = ?² - 4

⇒ 357 + 4 = ?²

⇒ 361 = ?²

⇒ ? = 19

∴ 19 will come in place of the question mark ('?').

Given:

162 + (5/8) of 344 + ? = 500

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

162 + (5/8) of 344 + ? = 500

⇒ 256 + (5/8) of 344 + ? = 500

⇒ 256 + 215 + ? = 500

⇒ ? = 500 - 471

⇒ ? = 29

∴ 29 should come in place of the question mark (?).

Given:

12.5% of 256 + 11.11% of 729 = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

12.5% of 256 + 11.11% of 729 = ?

⇒ (1/8) × 256 + (1/9) × 729 = ?

⇒ 32 + 81 = ?

⇒ ? = 113

∴ The value of '?' is 113.

Hint

Percentage to Fraction table

Given:

(19 × 23) × 16 ÷ 38 = ? × 8

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

(19 × 23) × 16 ÷ 38 = ? × 8

⇒ (19 × 23) × (16/38) = ? × 8

⇒ 23 × 8 = ? × 8

⇒ ? = 23

∴ The value of '?' will be 23.

Given: 

30% of 150 + ?% of 500 = 105

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

30% of 150 + ?% of 500 = 105

⇒ (30/100) × 150 + (?/100) × 500 = 105

⇒ 3 × 15 + ? × 5 = 105

⇒ ? × 5 = 105 - 45

⇒ ? × 5 = 60

⇒ ? = 12

∴ 12 will come in place of the question mark ('?').

The correct answer is: 3

Given:

8920 - 3708 + 1128 = 2619 + ?2

Calculation:

8920 - 3708 + 1128 = 2619 + ?2

⇒ 10048 - 3708 = 2619 + ?²

     6340 = 2619 + ?²

⇒ 3721 = ?²

⇒ ? = 61

∴ The value of '?' is 61

Solution :

 Given :

 ⇒ 444.44 + 44.44 + 41 + 0.44 + 0.04 = ?

 ⇒ 444.44 + 85.44 + 0.44 + 0.04 = ?

 ⇒ 444.44 + 85.44 + 0.48 = ?

 ⇒ 529.88 + 0.48 = ?

 ⇒ ? = 530.36

 Hence 530.36 is the correct answer.

 

Total number of electronic products (TV + Mobile + AC) sold by shop 'X' = (3/7) × (260 + 440) = 300

The number of ACs sold by shop 'X' = (7/25) × 300 = 84

Required ratio = 84 : 80 = 21 : 20

Hence, the correct answer is 21 : 20.

 

Total average revenue generated from the sale of TVs by all three electronic shops together = 40 × 10000 + 20 × 15000 + 80 × 25000 = 2700000 Rs.

Required total average revenue generated = 2700000/3 = 900000 Rs.

Hence, the correct answer is 900000 Rs.

 

The total number of 'Mobiles' (4G + 5G) sold by all three given shops = 340

The number of '4G' Mobiles sold by shop 'D' = 340 × 10% = 34

The number of '5G' Mobiles sold by shop 'D' = 340 - 34 = 306

Required difference = 306 - 100 = 206

Hence, the correct answer is 206.

 

The total number of electronic products (Online + Offline) sold by shop 'A' = 260

Let the number of 'Online' electronic products sold by shop 'A' = x

And, the number of 'Offline' electronic products sold by shop 'A' = y

ATQ, x + y = 260 ...(i)

And, y - x = 60 ...(ii)

Adding (i) + (ii) 

⇒ 2y = 320

⇒ y = 160

The number of 'Offline' electronic products sold by shop 'A' = y = 160

Required sum = 160 + 160 = 320

Hence, the correct answer is 320.

 

The number of 'Plasma' TVs sold by shop 'A' = 20% × 40 = 8

The number of 'LCD' TVs sold by shop 'A' = 40 - 8 = 32

Required% = (32/60) × 100 = 53.33%

Hence, the correct answer is 53.33%.

Given:

Distance between two places = 180km

Trains meet at the time = 4hrs

Concept used:

The relative speed between two trains if they are moving in opposite directions = (x + y)kmph

Distance = Time × speed

Calculation: 

Let the speed of the train starts from P place  = x kmph

let the speed of the train starts from Q place = y kmph

According to the information given in the question 

Distance between two places = 180km

Relative speed between trains = (x + y)kmph

The time after which the trains meet each other = 4hrs

Distance = Time × speed

180 = 4 × (x + y)

x + y =  45.......................................................... (1)

Now, according to the information in the given question

Difference between speeds of both trains

x - y = 13........................................................... (2)

Adding equations (1) and (2),

2x = 58

So, x = 29

Put this in equation (2),

29 - y = 13

y = 16.

So,

x = 29 , y = 16

Hence the speeds of both trains are 29kmph and 16kmph.

Shortcut Trick

Ratio of Mother to Son: Present = 4 : 1 and After 8 years = 16 : 5.

Equating ratio difference: (4:1)×11 and (16:5)×3 → 44:11 and 48:15.

Change in units = 15 − 11 = 4 units → 8 years. So, 1 unit = 2 years.

Present age of son = 11 units × 2 = 22 years.

Value of x = 22² = 484. Then, x + 2 = 484 + 2 = 486.

∴ The correct answer is 486.

Alternate Method

Given: Present ratio M : S = 4 : 1. Let ages be 4s and s.

Formula: Ratio = (Initial Age + Time) ÷ (Initial Age + Time)

⇒ (4s + 8) ÷ (s + 8) = 16 ÷ 5

⇒ 5 × (4s + 8) = 16 × (s + 8)

⇒ 20s + 40 = 16s + 128

⇒ 4s = 88

⇒ s = 22

⇒ x = s² = 22² = 484

⇒ x + 2 = 484 + 2 = 486

∴ The correct answer is 486.

Additional Information

Ratio Difference Method

To solve age problems quickly, ensure the difference between ratio parts remains constant over time by multiplying with the cross-difference.

Square of Numbers

Memorizing squares up to 30 helps in fast calculations. For example, 21² = 441, 22² = 484, 23² = 529.

Ages Property

The difference between the ages of two people always remains constant, regardless of how many years pass.

Given :

Difference between the SI and CI for 2 years = 224 Rs.

Rate of interest = 20%

Time period = 2 years

Calculation :

Difference between the SI and CI for 2 years = 224

⇒ P × (20/100)² = 224

⇒ P = 5600 Rs.

Hence, the correct answer is 5600 Rs.

Given:

Upstream distance = 10 km

Downstream distance = 25 km

Time taken in each case = 15 hours

Formula used:

Distance = speed × time

Calculation:

Let the man rows in still water at the rate of x km/hr 

And the rate of stream be y km/hr

Then, man's rate in downstream = (x + y) km/hr

And man's rate in upstream = (x - y) km/hr

∴ The time taken in downstream = 25/x + y 

And the time taken in upstream = 10/x - y

⇒25/(x + y) = 15   &   10/(x - y) = 15

⇒15x + 15y = 25   &   15x - 15y = 10

By adding these two,

30x = 35 

⇒x = 35/30 = 7/6 km/hr

By putting x = 35/30

15(35/30) + 15y = 25

⇒15y = 15/2

⇒y = 1/2 km/hr 

Now, L = x + y

⇒ 3/5 (L)= (7/6 + 1/2) × 3/5

⇒3/5 × 10/6 = 1

∴The value of (3/5)L is 1

 

The initial quantity of mixture = 343 litres

Initial ratio of mixture = 5 : 2

The final ratio of mixture = 5 : 3

Initial quantity of wine = 5 units

Initial quantity of water = 2 units

According to the question,

(5 + 2) units = 343 litres

⇒ 7 units = 343 litres

⇒ 1 unit = 49 litres

From the initial and final ratio of the mixture, we can see that quantity of water is increased by 1 unit.

So, the quantity of water added = 1 unit

⇒ 49 litres

∴ The quantity of water added is 49 litres.

Traditional Method:

Given:

The initial quantity of mixture = 343 litres

Initial ratio of mixture = 5 : 2

The final ratio of mixture = 5 : 3

Calculation:

Let initial quantity of wine and water be 5x and 2x.

5x + 2x = 343

⇒ 7x = 343

⇒ x = 49

Initial quantity of wine = 5x

⇒ 5 × 49

⇒ 245 litres

Initial quantity of sugar = 2x

⇒ 2 × 49

⇒ 98 litres

Let the water to be added in new mixture be x litres.

According to the question,

245/(98 + x) = 5/3

⇒ 245 × 3 = 5(98 + x)

⇒ 735 = 490 + 5x

⇒ 5x = 245

⇒ x = 49

∴ The quantity of water added is 49 litres.

 

Total enrollment in college 'A' = 150% × 120 = 180

Total enrollment in college 'B' = (6/5) × 180 = 216

Total enrollment of students in colleges 'A', 'P', 'S', and 'B' together = (180 + 340 + 300 + 216) = 1036

Required average = 1036/4 = 259

Hence, the correct answer is 259.

 

The combined student enrollment in the 'Architecture' course at colleges 'P', 'R', and 'S' = 160 + 140 + 120 = 420

The combined student enrollment in the 'Engineering' course at colleges 'P', 'R', and 'S' = 180 + 120 + 180 = 480

Required% = [(480 - 420)/480] × 100 = 12.5%

Hence, the correct answer is 12.5%.

 

Total enrollment fee for the 'Engineering' course in college 'P' = 180 × 59000 = 10620000 Rs.

Total enrollment fee for the 'Architecture' course in college 'P' = 160 × 69000 = 11040000 Rs.

Required difference = 11040000 - 10620000 = 420000 Rs.

Hence, the correct answer is 420000 Rs.

 

Students from the 'Engineering' course at college 'R' who cancelled their enrollment  = 20% × 120 = 24

The total student enrollment in college 'R' at the end of the year = (120 - 24) + 140 = 236

Students from the 'Engineering' course at college 'S' who cancelled their enrollment  = 25% × 180 = 45

The total student enrollment in college 'S' at the end of the year = (180 - 45) + 120 = 255

Required difference = 255 - 236 = 19

Hence, the correct answer is 19.

 

Students selected from the 'Engineering' course to represent the college 'Q' = 83.33% × 240 = 200

Students selected from the 'Architecture' course to represent the college 'Q' = 60% × 180 = 108

Required sum = 200 + 108 = 308

Hence, the correct answer is 308.

Given:

Area of square is = 625 m²

Calculation:

Let be assume the length of rectangle 3p, side of square 5p.

Area of square = (5p)²

⇒ 625 = 25p²

⇒ p = 5 m

Length of rectangle = 3 × 5 = 15 m

Area of rectangle = Length × breadth

⇒ 90 = 15 × breadth

⇒ Breadth = 6 m

∴ The required result is 6 m.

Given:

Total number of students = N

Students who play cricket = 69%

Students who play hockey = 49%

Students who play both cricket and hockey = 54

Concept:

Venn Diagram

Calculation:

Suppose, the number of students who play both cricket and hockey = x%

Therefore, students who play only cricket = (69 – x)%

Students who play only hockey = (49- x)%

⇒ (69 – x) + x% + (49 – x)% = 100%

⇒ 118% - x% = 100%

⇒ x% = 18%

Given 18% → 54

⇒ 1% → 3

⇒ 100% → 300

∴ N = 300