Question

if 12 men can do a peice of work in 40 days by working 8 hours per day how many men will take to do it 10 times the amount of work if they work for 40 hours per day for 15 days

Answer 1

$12 \times 40 \times 8 = \frac{40 \times m \times 15 } {10} \\ 12 \times 40 \times 8 = 4 \times 15 \times m \\ 3 \times 40 \times 8 = 15 \times m \\ 4 0 \times 8 = 5 \times m \\ 8 \times 8 = m \\ m = 64$

Answer 2

• 64 men will complete 10 times the amount of work if they work for 40 hours per day in 15 days .

Given :- 12 men can do a piece of work in 40 days by working 8 hours per day .

To Find :- How many men will take to do it 10 times the amount of work if they work for 40 hours per day for 15 days ?

Formula used :- If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day, then :-

• (M1 × D1 × H1)/W1 = (M2 × D2 × H2)/W2
• Or, M1 × D1 × H1 × W2 = M2 × D2 × H2 × W1 .

Solution :-

It is given that, 12 men can do a piece of work in 40 days by working 8 hours per day . So,

• M1 = 12 men
• D1 = 40 days
• H1 = 8 hours / day
• W1 = 1 piece of work .

Now, Let x men can complete 10 times the amount of work if they work for 40 hours per day for 15 days .

So,

• M2 = x men
• D2 = 15 days
• H1 = 40 hours / day { since 1 day has only 24 hours , it is not possible . But we will solve the problem with given data . }
• W2 = (1 × 10) = 10 piece of work .

then, putting all values in above told formula we get,

→ M1 × D1 × H1 × W2 = M2 × D2 × H2 × W1

→ 12 × 40 × 8 × 10 = x × 15 × 40 × 1

40 will be cancel from both sides ,

→ 12 × 8 × 10 = x × 15

dividing both sides by 5,

→ 12 × 8 × 2 = x × 3

dividing both sides by 3,

→ 4 × 8 × 2 = x

→ x = 64 men (Ans.)

Hence, 64 men are required to complete 10 times the amount of work in time .

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