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

16)

A man can do a piece of work in 5 days. With the help of his friend, he can do the same work in 3 days. In how many days can his friend complete the work ?

A)
6 days
B)
$6 \frac{1}{2}$ days
C)
$7 \frac{1}{2}$ days
D)
7 days
E)
None of these

Answer: Option C

Explanation

According to the question,

In 1 day,

A man and his friend can complete $\frac{1}{3}$ ^th of the work

Man can complete $\frac{1}{5}$ ^th of the work

His friend can complete the work $= \frac{1}{3} - \frac{1}{5} = \frac{2}{15}$

∴ His friend can complete the work in $\frac{15}{2} o r 7 \frac{1}{2}$ days.

Hence option C is the correct.

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Discussion

17)

A can complete a piece of work in 18 days and B can complete the same work in half time taken by A. Then, working together, what part of the same work they can complete in a day?

A)
$\frac{1}{6}$ ^thpart
B)
$\frac{1}{9}$ ^thpart
C)
$\frac{2}{7}$ ^th part
D)
$\frac{2}{9}$ ^thpart
E)
$\frac{2}{5}$ ^thpart

Answer: Option A

Explanation

According to the question,

In 1 day,

A can complete $\frac{1}{18}$ ^th of the work

B can complete $\frac{1}{9}$ ^th of the work

(A+B) together can complete $= \frac{1}{9} + \frac{1}{18} = \frac{3}{18} = \frac{1}{6}$ ^th of the work

Hence option A is the correct.

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Discussion

18)

'A' works twice as fast as 'B'. If both of them can together finish a work in 4 days, then in how many days, B alone can do it?

A)
12 days
B)
16 days
C)
11 days
D)
15 days
E)
None of these

Answer: Option A

Explanation

According to the question,

A does the work in x days and B can does the same work in 2x days.

$= \frac{1}{x} + \frac{1}{2 x} = \frac{1}{4}$

On multiplying both the sides with x we get,

$\Rightarrow 1 + \frac{1}{2} = \frac{x}{4} \Rightarrow \frac{3}{2} = \frac{x}{4} x = \frac{4 \times 3}{2} = 6 d a y s$

∴ B will finish the work in 2x days or in 2×6=12 days.

Hence option A is the correct.

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Discussion

19)

6 men or 10 women can do a piece of work in 24 days. How long will 12 men and 10 women take to finish the work?

A)
8 days
B)
7 days
C)
17 days
D)
5 days
E)
None of these

Answer: Option A

Explanation

According to the question,

6 men = 10 women

∴ 1 man = $\frac{10}{6}$ or $\frac{5}{3}$ women

Now, 12 men + 10 women $= 12 \times \frac{5}{3}$ women+ 10 women

⇒ 20 women+ 10 women = 30 women

According to the formula,

M₁ D₁ W₂ = M₂ D₂ W₁

Here,

M₁ = 10, D₁ =24, W₁ =1,

M₂ = 30, D₂ = ?, W₂= 1

$\Rightarrow 10 \times 24 \times 1 = 30 \times D_{2} \times 1 ∴ D_{2} = \frac{10 \times 24}{30} = 8 d a y s$

Hence, option A is the correct.

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Discussion

20)

A can do $\frac{1}{2}$ of the work in 5 days and B can do $\frac{2}{5}$ of the work in 10 days. In how many days both A and B together can do the work?

A)
$7 \frac{2}{7}$ days
B)
$7 \frac{1}{7}$ days
C)
$7 \frac{3}{7}$ days
D)
$7 \frac{5}{7}$ days
E)
None of these

Answer: Option B

Explanation

According to the question,

A completes the work in 5×2=10 days

B completes the work in $10 \times \frac{5}{2} = 25$ days

In 1 day,

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

B can complete $\frac{1}{25}$ ^th of the work

(A+B) together can complete $\frac{1}{10} + \frac{1}{25} = \frac{5 + 2}{50} = \frac{7}{50}$ ^th of the work

∴ (A+B) will complete the whole work in $\frac{50}{7}$ days.

∴ Required time = $\frac{50}{7}$ = $7 \frac{1}{7}$ days.

Hence option B is the correct.

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Discussion

Time and Work-Basic test 2

Answer: Option C

Answer: Option A

Answer: Option A

Answer: Option A

Answer: Option B