Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
What will come in the place of the question mark ‘?’ in the following question?
89% of 624 + 1220 – 1020 = ?
755.35
755.36
755.46
755.26
None of these
Correct answer
755.35
What will come in the place of the question mark '?' in the following question?
∛1728 × ∛4096 ÷ ∛512 = ?
24
36
30
12
16
Correct answer
24
What will come in the place of the question mark ‘?’ in the following question?
10 + 12 of 12 – 44 × 11 = ?
300
-297
-330
0
-280
Correct answer
300
What will come in the place of the question mark ‘?’ in the following question:
20% of 60 + 30% of 90 + 36 = ?
82
75
65
85
94
Correct answer
82
What will come in the place of the question mark ‘?’ in the following question:
35% of 180 + 45% of 180 = 180 – ?
40
42
36
48
50
Correct answer
40
The ratio of Milk and Water in the container is 3 : 2 . If 15 liter mixture is taken out and replaced by the Milk, the ratio become 3 : 1 then find the total quantity of mixture in the container is:
25 litres
20 litres
15 litres
Can't be determined
None of these
Correct answer
25 litres
In 2019, a person had an amount of ₹17,500, which increased by 20% every year. In 2021, the person spent 69% of the amount they had. What was the remaining savings?
₹8,812
₹7,812
₹9,812
₹6,812
₹4,812
Correct answer
₹8,812
A person invests a certain amount for 2 years at an interest rate of 20% per annum under compound interest. The same person invests the same amount for 2 years at a 30% interest rate under simple interest. The difference between the compound interest and simple interest after 2 years is ₹896. What is the invested amount?
₹6600
₹6700
₹5600
₹4600
₹5100
Correct answer
₹6600
Two articles have the same cost price. Article A is sold at a 20% profit, and Article B is sold at a 30% loss. The overall loss incurred is ₹50. At what price should Article B be sold so that the seller gets an overall 40% profit?
Rs. 800
Rs. 500
Rs. 700
Rs. 1000
Rs. 900
Correct answer
Rs. 800
A train with a speed of 72 km/h crosses a pole in 16 seconds. If the speed is increased by 12 m/s, calculate the time it will take to cross the pole.
20 seconds
30 seconds
50 seconds
10 seconds
60 seconds
Correct answer
20 seconds
The ratio of difference between CI and SI at r% for three years and 2 years is 25:8. Find the compound interest for Rs. 3200 2 years at [r + 7.5] % for 2 years?
1160
1408
1250
1640
1860
Correct answer
1408
Why this answer is correct
Calculation
The difference between CI and SI for 2 years at rate r% on principal P:
CI - SI (2 years) = [P × r2 / 1002]
For 3 years:
CI - SI (3 years) = [P × r2 / 1002] × [(300 + r) / 100]
Take ratio:
[ CI - SI for 3 years]/[CI - SI for 2 years] = 25/8
[(300 + r) / 100] = 25/8
So, 2400 + 8r = 2500
So, ⇒ r = 100 / 8 = 12.5%
Now rate of interest is 12.5 + 7.5 = 20%
Successive CI for 2 years at 20% per annum is 44%
So, required interest amount is 3200 × 44 /100 = 1408
Volume of the cylinder is 9240 m3. Radius of the cylinder [r + 4] m and height is 15 m. Find the sum of the volume of the cube and sphere if the side of the cube is 2r - 4 m and the radius of the sphere is r + 11?
48907
44504
46504
45804
42904
Correct answer
42904
Why this answer is correct
Calculation
Volume of cylinder = 9240 m³
Radius of cylinder = r+4
Height of cylinder = 15 m
Volume of cylinder = πr2h
Or, π(r + 4)2 × 15 = 9240
Or, ⇒ r + 4 = √196 = 14
⇒ r = 14 – 4 =10
Side of cube = 2r – 4 = 2 × 10 – 4 = 16
Volume = s3 =163 = 4096 m³
Radius = r + 11 = 10 + 11 = 21 m
Volume = [4/3] π r3 = [4/3] × [22/7] × 213 = 38808 m³
Total Volume (Cube + Sphere) = 4096 + 38808 = 42904 m³
The cost of a cap and sunglass is Rs 140 and Rs 110, respectively. The marked price of the cap and the sunglass is the same, and the discount allowed on the cap and the sunglass is 20% and 30%, respectively. If the overall profit is 20%, then find the marked price of the sunglass?
240
200
250
350
320
Correct answer
200
Why this answer is correct
Given:
Cost of cap = ₹140
Cost of sunglass = ₹110
Discount on cap = 20%
Discount on sunglass = 30%
Overall profit = 20%
Formula used:
Marked price (M) = Cost price / (1 - Discount%)
Overall profit = (Total selling price - Total cost price) / Total cost price
Calculations:
Let the marked price of both cap and sunglass be M.
Selling price of cap = M × (1 - 0.20) = 0.80M
Selling price of sunglass = M × (1 - 0.30) = 0.70M
Overall profit = 20% ⇒ (Total selling price - Total cost price) / Total cost price = 0.20
⇒ (0.80M + 0.70M - 140 - 110) / (140 + 110) = 0.20
⇒ (1.50M - 250) / 250 = 0.20
⇒ 1.50M - 250 = 50
⇒ 1.50M = 300
⇒ M = 300 / 1.50 = 200
∴ The marked price of the sunglass is ₹200.
Four shops—A, B, C, and D—manufacture and sell items of the same kind. Shop A sold twice as many items as it left unsold. The number of items produced in Shop B is 20 more than Shop A, Shop C produced 33.33% less items as number of items produced by A. Number of unsold items in shop B is 25% more than the same in shop A. Number of sold item in shop C is 2/3rd of total unsold items of shop A and B together. Number of unsold items in shop D is double of the number of unsold items in shop C. Shop D produced 12.5% more items than number of items produced in shop C. Number of item produced in shop A is 120.
Out of the total items produced by Shop A, the ratio of gadget items to plastic items is 5:3. If the number of plastic items sold by Shop A is 12, then find the number of unsold gadget items in Shop A.
2
7
5
4
3
Correct answer
7
Why this answer is correct
Common Calculation
Shop A produced = 120
Shop A sold = 2× unsold
Let unsold = x ⇒ sold = 2x
So, total = x + 2x = 3x ⇒ 3x = 120 ⇒ x = 40, sold = 80
Shop B:
Produced = A + 20 = 120 + 20 = 140
Unsold in B = 25% more than unsold in A = 40 + 25% of 40 = 40 + 10 = 50
Sold = 140 - 50 = 90
Shop C:
Produced = 33.33% less than A = 120 - (1/3 × 120) = 120 - 40 = 80
Now:
Total unsold in A + B = 40 + 50 = 90
Sold in C = (2/3) × 90 = 60
So, Unsold = 80 - 60 = 20
Shop D:
Unsold = 2 × unsold in C = 2 × 20 = 40
Produced = 12.5% more than produced in C = 80 + 12.5% of 80 = 80 + 10 = 90
Sold = 90 - 40 = 50
| Shop | Total number of items produced | Total number of items sold | Total number of items unsold |
|---|---|---|---|
| A | 120 | 80 | 40 |
| B | 140 | 90 | 50 |
| C | 80 | 60 | 20 |
| D | 90 | 50 | 40 |
Calculation
In shop A, Gadget : Plastic = 5 : 3 in 120 items
Total parts = 5 + 3 = 8
Gadget items = (5/8) × 120 = 75
Plastic items = (3/8) × 120 = 45
Plastic sold = 12 ⇒ Plastic unsold = 45 - 12 = 33
Total unsold in A = 40
⇒ Gadget unsold = 40 - 33 = 7
Four shops—A, B, C, and D—manufacture and sell items of the same kind. Shop A sold twice as many items as it left unsold. The number of items produced in Shop B is 20 more than Shop A, Shop C produced 33.33% less items as number of items produced by A. Number of unsold items in shop B is 25% more than the same in shop A. Number of sold item in shop C is 2/3rd of total unsold items of shop A and B together. Number of unsold items in shop D is double of the number of unsold items in shop C. Shop D produced 12.5% more items than number of items produced in shop C. Number of item produced in shop A is 120.
If the number of items sold by Shop F is [2/3]rd of the total number of items sold by Shop B and C together, Shop F sold 50% of items. Find the number of items produced in F?
290
300
200
250
260
Correct answer
200
Why this answer is correct
Common Calculation
Shop A produced = 120
Shop A sold = 2× unsold
Let unsold = x ⇒ sold = 2x
So, total = x + 2x = 3x ⇒ 3x = 120 ⇒ x = 40, sold = 80
Shop B:
Produced = A + 20 = 120 + 20 = 140
Unsold in B = 25% more than unsold in A = 40 + 25% of 40 = 40 + 10 = 50
Sold = 140 - 50 = 90
Shop C:
Produced = 33.33% less than A = 120 - (1/3 × 120) = 120 - 40 = 80
Now:
Total unsold in A + B = 40 + 50 = 90
Sold in C = (2/3) × 90 = 60
So, Unsold = 80 - 60 = 20
Shop D:
Unsold = 2 × unsold in C = 2 × 20 = 40
Produced = 12.5% more than produced in C = 80 + 12.5% of 80 = 80 + 10 = 90
Sold = 90 - 40 = 50
| Shop | Total number of items produced | Total number of items sold | Total number of items unsold |
|---|---|---|---|
| A | 120 | 80 | 40 |
| B | 140 | 90 | 50 |
| C | 80 | 60 | 20 |
| D | 90 | 50 | 40 |
Calculation
Given:
Number of items sold by Shop B = 90 (from the table)
Number of items sold by Shop C = 60 (from the table)
Number of items sold by Shop F = (2/3) × (Total items sold by Shop B and C together)
Shop F sold 50% of the items it produced
Calculations:
Total items sold by Shop B and C together = 90 + 60 = 150
Number of items sold by Shop F = (2/3) × 150 = 100
Since Shop F sold 50% of the items it produced, let the total number of items produced by Shop F be x:
50% of x = 100
⇒ x = 100 × 2 = 200
The total number of items produced in Shop F is 200.
Four shops—A, B, C, and D—manufacture and sell items of the same kind. Shop A sold twice as many items as it left unsold. The number of items produced in Shop B is 20 more than Shop A, Shop C produced 33.33% less items as number of items produced by A. Number of unsold items in shop B is 25% more than the same in shop A. Number of sold item in shop C is 2/3rd of total unsold items of shop A and B together. Number of unsold items in shop D is double of the number of unsold items in shop C. Shop D produced 12.5% more items than number of items produced in shop C. Number of item produced in shop A is 120.
The number of unsold items in Shop A is approximately what percentage of the total items produced in Shop B?
44.44%
28.57%
22.5%
12.5%
37.5%
Correct answer
28.57%
Why this answer is correct
Common Calculation
Shop A produced = 120
Shop A sold = 2× unsold
Let unsold = x ⇒ sold = 2x
So, total = x + 2x = 3x ⇒ 3x = 120 ⇒ x = 40, sold = 80
Shop B:
Produced = A + 20 = 120 + 20 = 140
Unsold in B = 25% more than unsold in A = 40 + 25% of 40 = 40 + 10 = 50
Sold = 140 - 50 = 90
Shop C:
Produced = 33.33% less than A = 120 - (1/3 × 120) = 120 - 40 = 80
Now:
Total unsold in A + B = 40 + 50 = 90
Sold in C = (2/3) × 90 = 60
So, Unsold = 80 - 60 = 20
Shop D:
Unsold = 2 × unsold in C = 2 × 20 = 40
Produced = 12.5% more than produced in C = 80 + 12.5% of 80 = 80 + 10 = 90
Sold = 90 - 40 = 50
| Shop | Total number of items produced | Total number of items sold | Total number of items unsold |
|---|---|---|---|
| A | 120 | 80 | 40 |
| B | 140 | 90 | 50 |
| C | 80 | 60 | 20 |
| D | 90 | 50 | 40 |
Calculation
Number of items unsold in A is 40
Number of items produced in B is 140
Percentage = (40 / 140) × 100 = 28.57%
Four shops—A, B, C, and D—manufacture and sell items of the same kind. Shop A sold twice as many items as it left unsold. The number of items produced in Shop B is 20 more than Shop A, Shop C produced 33.33% less items as number of items produced by A. Number of unsold items in shop B is 25% more than the same in shop A. Number of sold item in shop C is 2/3rd of total unsold items of shop A and B together. Number of unsold items in shop D is double of the number of unsold items in shop C. Shop D produced 12.5% more items than number of items produced in shop C. Number of item produced in shop A is 120.
Let the difference in sold items between Shop A and B be a. The number of items sold by Shop C is 2y, Find the value of a + y?
120
40
60
85
90
Correct answer
40
Why this answer is correct
Common Calculation
Shop A produced = 120
Shop A sold = 2× unsold
Let unsold = x ⇒ sold = 2x
So, total = x + 2x = 3x ⇒ 3x = 120 ⇒ x = 40, sold = 80
Shop B:
Produced = A + 20 = 120 + 20 = 140
Unsold in B = 25% more than unsold in A = 40 + 25% of 40 = 40 + 10 = 50
Sold = 140 - 50 = 90
Shop C:
Produced = 33.33% less than A = 120 - (1/3 × 120) = 120 - 40 = 80
Now:
Total unsold in A + B = 40 + 50 = 90
Sold in C = (2/3) × 90 = 60
So, Unsold = 80 - 60 = 20
Shop D:
Unsold = 2 × unsold in C = 2 × 20 = 40
Produced = 12.5% more than produced in C = 80 + 12.5% of 80 = 80 + 10 = 90
Sold = 90 - 40 = 50
| Shop | Total number of items produced | Total number of items sold | Total number of items unsold |
|---|---|---|---|
| A | 120 | 80 | 40 |
| B | 140 | 90 | 50 |
| C | 80 | 60 | 20 |
| D | 90 | 50 | 40 |
Calculation
A sold = 80, B sold = 90
⇒ Difference a = 90 - 80 = 10
C sold = 60
⇒ 60 = 2y ⇒ y = 30
a + y = 10 + 30 = 40
Four shops—A, B, C, and D—manufacture and sell items of the same kind. Shop A sold twice as many items as it left unsold. The number of items produced in Shop B is 20 more than Shop A, Shop C produced 33.33% less items as number of items produced by A. Number of unsold items in shop B is 25% more than the same in shop A. Number of sold item in shop C is 2/3rd of total unsold items of shop A and B together. Number of unsold items in shop D is double of the number of unsold items in shop C. Shop D produced 12.5% more items than number of items produced in shop C. Number of item produced in shop A is 120.
Number of items produced in Shop E is 33.33% more than the number produced in Shop D. If the ratio of sold to unsold items in E is 3:1, find the number of some unsold items in D and E.
70
75
65
55
80
Correct answer
70
Why this answer is correct
Common Calculation
Shop A produced = 120
Shop A sold = 2× unsold
Let unsold = x ⇒ sold = 2x
So, total = x + 2x = 3x ⇒ 3x = 120 ⇒ x = 40, sold = 80
Shop B:
Produced = A + 20 = 120 + 20 = 140
Unsold in B = 25% more than unsold in A = 40 + 25% of 40 = 40 + 10 = 50
Sold = 140 - 50 = 90
Shop C:
Produced = 33.33% less than A = 120 - (1/3 × 120) = 120 - 40 = 80
Now:
Total unsold in A + B = 40 + 50 = 90
Sold in C = (2/3) × 90 = 60
So, Unsold = 80 - 60 = 20
Shop D:
Unsold = 2 × unsold in C = 2 × 20 = 40
Produced = 12.5% more than produced in C = 80 + 12.5% of 80 = 80 + 10 = 90
Sold = 90 - 40 = 50
| Shop | Total number of items produced | Total number of items sold | Total number of items unsold |
|---|---|---|---|
| A | 120 | 80 | 40 |
| B | 140 | 90 | 50 |
| C | 80 | 60 | 20 |
| D | 90 | 50 | 40 |
Calculation
D produced = 90
⇒ E produced = 90 + 33.33% of 90 = 90 + 30 = 120
Sold : Unsold = 3:1 ⇒ Total = 4 parts
So, Unsold in E = (1/4) × 120 = 30
D unsold = 40
⇒ Total unsold in D and E = 40 + 30 = 70
A boat can cover 120 km downstream in 2.5 hours, and the speed of the boat and speed of stream in the ratio 7:5. If the boat can cover d-24 km upstream in 7.5 hours, then find the time taken by the boat to cover d km in still water?
7
5
4
3.5
3
Correct answer
3
Why this answer is correct
Given:
Downstream distance = 120 km, Time taken = 2.5 hours
Speed ratio of boat and stream = 7:5
Upstream distance = d - 24 km, Time taken = 7.5 hours
Formula used:
Speed downstream = (Speed of boat + Speed of stream)
Speed upstream = (Speed of boat - Speed of stream)
Speed = Distance / Time
Calculations:
Speed downstream = 120 km / 2.5 hours = 48 km/h
Let the speed of the boat = 7x and speed of stream = 5x
⇒ Speed downstream = 7x + 5x = 12x
⇒ 12x = 48
⇒ x = 4
Speed of boat = 7x = 7 × 4 = 28 km/h
Speed of stream = 5x = 5 × 4 = 20 km/h
Now, Speed upstream = Speed of boat - Speed of stream = 28 - 20 = 8 km/h
Distance upstream = d - 24 km, Time taken = 7.5 hours
Speed upstream = (d - 24) / 7.5
⇒ 8 = (d - 24) / 7.5
⇒ 8 × 7.5 = d - 24
⇒ 60 = d - 24
⇒ d = 84 km
Now, the time taken to cover d km in still water is given by:
Time = Distance / Speed of boat
Time = 84 km / 28 km/h = 3 hours
∴ The time taken by the boat to cover d km in still water is 3 hours.
P and Q started a business, and the investment of P is Rs 2000 more than that of Q. P investment for 8 months and Q investment for a year. If at the end of the year the total profit is Rs 6300, then find the investment of Q. (
Note:
The profit share of P is 16x, where x = 152 - 50]
12500
16500
18500
10500
10000
Correct answer
10000
Why this answer is correct
Calculation
P and Q start a business.
P's investment is ₹2000 more than Q's.
P invests for 8 months, Q for 12 months.
Total profit at the end of the year = ₹6300.
Profit share of P is 16x, where
x=152 – 50 = 225 – 50 = 175
So, P's share = 16 × 175 =₹2800
Total profit = 6300
⇒Q’s share = 6300 – 2800 =3500
Let investment of Q = ₹y
→ Then P’s investment = ₹(y + 2000)
So:
P = (y+2000) ×8
Q = y×12
Profit ratio = P : Q = 2800 : 3500 = 4 : 5
So:
[ (y+2000) × 8 ]/ 12y = 4/5
So, [(5 × 8) (y + 2000)] = 4 × 12y
⇒ 40y + 80000 = 48y
⇒ 80000 = [48y − 40y] = 8y
⇒ y = 80000/8 = 10,000
Investment of Q = 10,000
Solving previous year questions by topic helps identify recurring concepts, question patterns, and frequently asked sub-topics. Attempt each question, review the step-by-step explanation, and note down key formulas or facts for quick revision before the exam.