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Given:

A man travels from A to B at a speed of 36 km/hr in 74 minutes and he travels a distance from B to C with a speed of 45 km/hr in 111 minutes. 

Formula used:

Average speed = Total distance/Total time taken

Calculation:

Time taken = 74 min : 111 min   [given]

Ratio of Time taken = 2 : 3

Average Speed = \(\frac{{36\ \times\ 2\ +\ 45\ \times\ 3}}{{2\ +\ 3}}\)

Average Speed = 207/5

Average Speed = 41.4 km/hr

∴ The average speed of whole journey is 41.4 km/h

Given:

The area of the circle = 154 m²

The perimeter of the square is equal to the circumference of the circle.

Formula Used:

The area of the circle = πr²

The circumference of the circle = 2πr

The perimeter of the square = 4 × a

Where, a = side of the square, and r = radius of the circle 

Calculation:

The area of the circle = 154 m²

⇒ πr² = 154

⇒ (22/7) × r² = 154

⇒ r² = (154 × 7)/22

⇒ r = √49

⇒ r = 7 m

The circumference of the circle = 2πr

⇒ 2 × (22/7) × 7

⇒ 44

The perimeter of the square = The circumference of the circle

⇒ 4 × a = 44

⇒ a = 44/4

⇒ a = 11 m

∴ The side of the square is 11 m.

Shortcut Trick

Present ratio of Ram and Ramesh = 3 : 5 (Difference = 2 units).

Ratio after 7 years = 4 : 5 (Difference = 1 unit).

To equate differences, multiply the future ratio by 2: (4 : 5) × 2 = 8 : 10.

Change in Ramesh’s age units = 10 − 5 = 5 units.

Given that 5 units = 7 years, then Ramesh’s present age (5 units) is 7 years.

∴ The correct answer is 7 years.

Alternate Method

Given:

Present age ratio of Ram and Ramesh = 3 : 5

Ratio after 7 years = 4 : 5

Calculations:

⇒ Let the present ages of Ram and Ramesh be 3x and 5x respectively.

⇒ After 7 years, their ages will be (3x + 7) and (5x + 7).

⇒ According to the problem: (3x + 7) ÷ (5x + 7) = 4 ÷ 5

⇒ 5 × (3x + 7) = 4 × (5x + 7)

⇒ 15x + 35 = 20x + 28

⇒ 20x − 15x = 35 − 28

⇒ 5x = 7

⇒ Ramesh’s present age = 5x = 7 years.

∴ The correct answer is 7 years.

Additional Information

Age Difference Consistency

The difference between the ages of two individuals remains constant throughout their lives. If the difference is 'd' now, it will remain 'd' after any number of years.

Ratio Adjustment Method

When the time gap is the same for both people, adjust the ratios such that the numerical difference between the terms of each ratio is identical.

Cross-Multiplication in Ratios

For a ratio a : b changing to c : d after 'n' years, the value of one part x = [n × (d − c)] ÷ [ad − bc].

Let the speed of boat in still water be x km/hr

Speed of stream = y km/hr

Speed upstream = (x - y) km/hr

(x - y) = 35/7 = 5      ----(1)

Speed downstream = (x + y) km/hr

(x + y) = 35/5 = 7       ----(2)

From (1) and (2), we get x = 6 km/hr

Speed of boat in still water = 6 km/hr

Given:

Coins = 480 

Conis of 1 Rupee, 50 Paise & 25 Paise

Value ration = 2 : 3 : 4

Calculation:

Ratio  =  1 Rs : 50 p : 25 p

Value =     2 : 3 : 4

Coin   =     2 : 6 : 16

⇒ 1 : 3 : 8

Total coins are 12x

⇒ 12x = 480

⇒ x = 480/12

⇒ x = 40

⇒ 1 : 3 : 8

⇒ 40 : 120 : 320

Coin of 1 Rupee = 40 

Coin of 50 Paise = 120

Coin of 25 Paise = 320

The value of 40 coins of 1 rupee is Rs.40

The value of 120 coins of 50 paise is Rs.60

The value of 320 coins of 25 paise is Rs.80

Total Value is (40 + 60 + 80) = 180

∴ The answer is Rs.180.

Alternate Method Let the value of 1 Rupee, 50 Paise, and 25 Paise coins be 2x, 3x, and 4x respectively.

Number of coins = Total value/value of each coin

Therefore,

Number of 1 Rupees coins = 2x/1 = 2x 

Number of 50 paise coins = 3x/(1/2) = = (3x) × 2 = 6x 

Number of 25 paise coins = 4x/(1/4) = = (4x) × 4 = 16x  

Since total number of coins = 480

2x + 6x + 16x = 480

24x = 480

x = 20

Therefore, the total amount 

⇒ 2x + 3x + 4x = 9x 

⇒ 9 × 20 = 180 Rs.

Shortcut Trick  

Total value of all coins together = Rs. (40 + 60 + 80) = Rs. 180

Calculation:

⇒ 100% = 2500

⇒ 1% = 25

Laptops sold by company A = 40% = 40 × 25 = 1000

Laptops sold by company C = 8% = 8 × 25 = 200

Difference between the sale of laptops of company A and C = 1000 - 200 = 800

∴ The correct answer is 800.

Given:

The length of the train is 300 m

The length of the bridge is 500 m

Concept:

Speed = Distance/Time

Calculation:

Let be assume the speed of the train is S

⇒ S = (300 + 500)/8 = 800/8 = 100 m/s

⇒ Now, time is taken by train to cross 600m long bridge = (300 + 600)/100 = 900/100 = 9 seconds

∴ The required result will be 9 seconds.

Sum of age of 11 members of a family = 22 × 11 = 242

Before 2 year the sum of ages of all family members = 242 – 22 = 220 (before 2 years, ages of all family members will be less than 2 years. Hence, overall reduction in age = 11 × 2 = 22)

Now, there are only 10 members in the family, hence average age = 220/10 = 22

Given:

SP for each phone = ₹ 18,000

Loss on the first phone = 10%

Profit on the second phone = 20%

Concept Used:

Profit = SP – CP

Loss = CP – SP

Profit% or Loss% = [(Profit or Loss)/CP] × 100

CP = (100 × SP)/(100 - loss%)

CP = (100 × SP)/(100 + profit%)

Calculation:

Net SP = ₹ 18,000 + 18,000 = ₹ 36,000

Net CP = ₹ 20,000 + 15,000 = ₹ 35,000

Here, SP > CP

So, Profit = 36,000 – 35,000 = ₹ 1000

GIVEN:

Four bells ring simultaneously at starting and an interval of 6 sec, 12 sec, 15 sec and 20 sec respectively.

CONCEPT:

LCM: It is a number which is a multiple of two or more numbers.

CALCULATION:

LCM of (6, 12, 15, 20) = 60

All 4 bells ring together again after every 60 seconds

Now,

In 2 Hours, they ring together = [(2 × 60 × 60)/60] times + 1 (at the starting) = 121 times

∴ In 2 hours they ring together for 121 times

Mistake Points

In these type of question we assume that we have started counting the time after first ringing. Due to this when we calculate the LCM it gives us the ringing at 2^nd time not the first time. So, we needed to add 1.