Time and Work-Basic level test 2 Solved previous year questions with detailed explanations

11)

8 men can do a piece of work in 10 days. How many men are needed to complete the work in 40 days?

A)
8 men
B)
2 men
C)
6 men
D)
9 men
E)
None of these

Answer: Option B

Explanation

Here,

M₁ = 8, D₁ =10, W₂ =1

M₂ = ?, D₂ = 40, W₁= 1

So according to the formula,

M₁ D₁ W₂ = M₂ D₂ W₁

$8 \times 10 \times 1 = M_{2} \times 40 \times 1 ⇨ M_{2} = \frac{8 \times 10}{40} = 2 m e n$

Hence option B is the correct.

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Discussion

12)

10 men can make 16 toys in 6 days working 3 hours a day. In how many days can 12 persons make 40 toys working 8 hours a day ?

A)
$4 \frac{13}{16}$
B)
$4 \frac{11}{16}$
C)
$4 \frac{7}{16}$
D)
$4 \frac{5}{16}$
E)
None of these

Answer: Option B

Explanation

Here,

M₁ = 10, D₁ =6, W₁ =40, T₁= 3

M₂ = 12, D₂ = ?, W₂= 16, T₂= 8

So according to the formula,

M₁ D₁ W₂ = M₂ D₂ W₁

$\Rightarrow 10 \times 6 \times 3 \times 40 = 12 \times D_{2} 8 \times 16 ∴ D_{2} = \frac{10 \times 6 \times 3 \times 40}{12 \times 8 \times 16} = \frac{75}{16} = 4 \frac{11}{16} d a y s$

Hence, option B is the correct.

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Discussion

13)

A can do a piece of work in 8 hours while B alone can do it in 16 hrs. In how many hours, Both A and B working together can finish the work ?

A)
$5 \frac{2}{3}$ hours
B)
$5 \frac{3}{5}$ hours
C)
$5 \frac{1}{5}$ hours
D)
$5 \frac{1}{3}$ hours
E)
None of these

Answer: Option D

Explanation

According to the question,

In 1 hour,

A can complete $\frac{1}{8}$ ^th of the work

B can complete $\frac{1}{16}$ ^th of the work

(A+B) together can complete $\frac{1}{8} + \frac{1}{16} = \frac{2 + 1}{16} = \frac{3}{16}$ ^th of the work

∴ (A+B) will complete the work in $\frac{16}{3} or 5 \frac{1}{3} h o u r s$

Hence option D is the correct.

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Work and Time

Discussion

14)

A can do a piece of work in 8 days, B can do it in 10 days and C can do it in 20 days. In how many days an A, B and C together complete the work ?

A)
$3 \frac{7}{11}$ days
B)
$3 \frac{5}{11}$ days
C)
$3 \frac{2}{11}$ days
D)
$3 \frac{9}{11}$ days
E)
None of these

Answer: Option A

Explanation

According to the question,

In 1 day,

A can complete $\frac{1}{8}$ ^th part of the work

B can complete $\frac{1}{10}$ ^th part of the work

C can complete $\frac{1}{20}$ ^th part of the work

(A+B+C)'s 1 day's work

$= \frac{1}{8} + \frac{1}{10} + \frac{1}{20} = \frac{5 + 4 + 2}{40} = \frac{11}{40}$

∴ (A+B+C) can finish the work in $\frac{40}{11}$ or $3 \frac{7}{11}$ days.

Hence option A is the correct.

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Discussion

15)

A and B can together do a piece of work in 18 days and A alone can do it in 36 days. In how many days B alone can do it ?

A)
35 days
B)
25 days
C)
36 days
D)
39 days
E)
None of these

Answer: Option C

Explanation

According to the question,

In 1 day,

(A+B) can complete $\frac{1}{18}$ ^th of the work

A can complete $\frac{1}{36}$ ^th of the work

B alone can complete,

$= \frac{1}{18} - \frac{1}{36} = \frac{2 - 1}{36} = \frac{1}{36}$

∴ B alone can finish the work in 36 days.

Hence option C is the correct.

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Discussion

Time and Work-Basic test 2

Answer: Option B

Answer: Option B

Answer: Option D

Answer: Option A

Answer: Option C