Numerical Ability Test - 7

Given:

Time taken by A to complete 3/7 of the work = 9 days

Time taken by B to complete 1/3 of the work = 14 days

Calculation:

A complete 3/7 of the work in 9 days

Time taken by A to complete the whole work = 9/(3/7) = 21 days

B complete 1/3 work in 14 days

Time taken by B to complete the whole work = 14/(1/3) = 42 days

Total work = L.C.M. (21, 42) = 42 units

Combined efficiency of A and B = (42/21) + (42/42)

⇒ Combined efficiency of A and B = 2 + 1 = 3 units/day

Time taken by A and B to complete the whole work = 42/3

⇒ Time taken by A and B to complete the whole work = 14 days

∴ The time taken by A and B to complete the work is 14 days.

Given:

Time taken by A to complete the work = 12 days

Time taken by B to complete the work = 21 days

Calculation:

Total work = L.C.M. of (12, 21) = 84 units

Efficiency of A = 84/12 = 7 units/day

Efficiency of B = 84/21 = 4 units/day

Combined efficiency of A and B = (7 + 4) = 11 units/day

Time taken by A and B working together = 84/11 days

∴ The time taken by A and B working together is 84/11 days.

Given:

50 men can build a wall in 120 days working 24 hours per day

Formula used:

m₁ × d₁ × h₁ = m₂ × d₂ × h₂

Where,

m₁ = Men₁, d1 = Days₁, 

m₂ = Men₂ = 10, d₂ = Days₂

Calculation:

According to the question:
50 × 120 × 24 = m₂ × 300 × 16

⇒ m₂ = 30

∴ 30 men will be required.

Given:

1/P + 1/Q = 1/48

Calculation:

Let time taken by P be a days and time taken by Q be 2a days.

⇒ 1/a + 1/2a = 1/48

⇒ 3/2a = 1/48

⇒ a = 72

∴ In 72 days, P alone can finish work.

Given:

A can do a piece of work in 12 days while B alone can do it in 8 days

Formula used:

The efficiency of a person is the inverse of the time taken

Calculation:

Let the total time taken together by both of them = t

Then, time taken by 

\( \dfrac{1}{t} = \dfrac{1}{12} + \dfrac{1}{8}\)

⇒ 1/t = 5/24

⇒ t = 24/5 

Then time taken for 5 times of the work = \( \dfrac{24}{5} \times 5\)

∴ Together they can finish 5 times of work in 24 days

Given:

P and Q can do the work = 12 days

P can do the work = 20 days

Calculate:

According to Question

\({1\over P} + {1\over Q} = {1\over 12}\)      

\({1\over 20} + {1\over Q} = {1\over 12}\)

\({1\over Q} = {1\over 12} - {1\over 20} \)

\({1\over Q} = {5-3\over 60} \)

Q = 60/2 = 30

Time taken by Q to complete the work in 30 days.

1/X = 1/A + 1/B

Where X is the time taken by A and B to fill the tank if they work together.

Let the time taken by both pipes be X hours.

1/X = 1/16 + 1/48 ⇒ (3 + 1)/48 ⇒ 1/X = 1/12 ⇒ X = 12

∴ The time taken by both pipes to fill the tank is 12 hours

Given :

A pipe can fill a cistern in 12 hours and another pipe can empty it completely in 18 hours. 

Concept used :

Total time taken = Total work/Work per unit time

Calculations :

Total work = LCM of 12 and 18 = 36 units 

Work done by Fill type per hour

⇒ 36/12 = 3 units 

Work done by empty pipe

⇒ 36/18 = - 2 units (-ve sign as they are working in opposite direction)

Total work per hour by them

⇒ 3 - 2 = 1 unit 

Time taken by both pipes to complete the work = 36/1 

⇒ 36 hours 

⇒ 36 The cistern will be filled in 36 hours.

Given:

Ram and Rahim complete a work in 15 days and 20 days respectively.

Total wage = Rs. 3500

Concept used:

Ratio of efficiency = Ration of wages

Calculation:

According to the question, we have

Ratio of their efficiency = 4 : 3

According to the concept, we have

Ratio of their wages = 4 : 3

Let the wage of Ram be 4x and the wage of Rahim be 3x

So, According to the question, we have

4x + 3x = Rs. 3500

⇒ 7x = Rs. 3500

⇒ x = Rs. 500

So, the wage of Ram is 4x = Rs. (4 × 500)

⇒ Rs. 2000

∴ Ram gets Rs. 2000 as his share.

Given:

40 workers can build a dam in 30 days

60 workers are to be assigned to complete the same work

Formula used:

Efficiency = work done/Time taken

Calculation:

Let the number of days be x

40 workers can build a dam in 30 days = 40 × 30

⇒ 1200

Now,

60 Workers are to be assigned to be complete the same work 

⇒ x = 1200/60

⇒ 20 days

∴ The number of days required will be 20