Time and Work
- Tapas works twice as fast as Mihir. If both of them together complete a work in 12 days, Tapas alone can complete it in
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Using Rule 2,
If Tapas alone takes x days to complete the work, then= 1 + 1 = 1 x 2x 12 ⇒ 2 + 1 = 1 2x 12
⇒ 2x = 36
⇒ x = 18 daysCorrect Option: B
Using Rule 2,
If Tapas alone takes x days to complete the work, then= 1 + 1 = 1 x 2x 12 ⇒ 2 + 1 = 1 2x 12
⇒ 2x = 36
⇒ x = 18 days
- A and B together can complete a work in 15 days. A is 50% more efficient worker than B. How long will A take to complete the work alone ?
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Ratio of the work of A and B
done in 1 day = 3 : 2
[∵ B's work doen = x (let), thenA's work done = x + 50 x = 3 x 100 2 So, (A : B)'s work done = 3 x : x or 3 : 2] 2
∵ Work done by A and B together in 1 day= 1 15 ∴ A’s 1 day’s work = 1 × 3 15 5 = 1 25
Hence, A alone will finish the work in 25 days.
Aliter : Using Rule 22,Here, n = 3 2
because A is 50% more efficient than B.
D = 15
Time taken by A= 
n + 1 
× D n = (3/2) + 1 × 15 = 25 days 3/2 Correct Option: E
Ratio of the work of A and B
done in 1 day = 3 : 2
[∵ B's work doen = x (let), thenA's work done = x + 50 x = 3 x 100 2 So, (A : B)'s work done = 3 x : x or 3 : 2] 2
∵ Work done by A and B together in 1 day= 1 15 ∴ A’s 1 day’s work = 1 × 3 15 5 = 1 25
Hence, A alone will finish the work in 25 days.
Aliter : Using Rule 22,Here, n = 3 2
because A is 50% more efficient than B.
D = 15
Time taken by A= n + 1 × D n = (3/2) + 1 × 15 = 25 days 3/2
- A is twice as good a workman as B and B is twice as good a workman as C. If A and B can together finish a piece of work in 4 days, then C can do it by himself in
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Using basics of Rule 2,
According to the question,
If A takes x days to complete the work, B will take 2x days and C will take 4x days,
Now, (A + B)'s 1 day’s work= 1 4 = 1 + 2 = 1 x 2x 4 ⇒ 2 + 1 = 1 2x 4
⇒ 2x = 12 ⇒ x = 6
∴ C will complete the work in 4x
i.e. 24 days.
Correct Option: C
Using basics of Rule 2,
According to the question,
If A takes x days to complete the work, B will take 2x days and C will take 4x days,
Now, (A + B)'s 1 day’s work= 1 4 = 1 + 2 = 1 x 2x 4 ⇒ 2 + 1 = 1 2x 4
⇒ 2x = 12 ⇒ x = 6
∴ C will complete the work in 4x
i.e. 24 days.
- To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it ?
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Using basics of Rule 2,
Let B alone can do the work in x days∴ A can do the work in 3x days. 2
According to the question,= 1 + 2 = 1 x 3x 18 ⇒ 3 + 2 = 1 3x 18 ⇒ 5 = 1 3x 18
⇒ 3x = 18 × 5⇒ x = 18 × 5 = 30 days 3 Correct Option: A
Using basics of Rule 2,
Let B alone can do the work in x days∴ A can do the work in 3x days. 2
According to the question,= 1 + 2 = 1 x 3x 18 ⇒ 3 + 2 = 1 3x 18 ⇒ 5 = 1 3x 18
⇒ 3x = 18 × 5⇒ x = 18 × 5 = 30 days 3
- A 10 hectare field is reaped by 2 men, 3 women and 4 children together in 10 days. If working capabilities of a man, a woman and a child are in the ratio 5 : 4 : 2, then a 16 hectare field will be reaped by 6 men,4 women and 7 children in
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Using Rule 1,
Ratio of the working capabilities of a man, a woman and a child = 5 : 4 : 2
∴ Ratio of man, woman and child equivalence= 1 : 1 : 1 5 4 2 = 1 × 20 : 1 × 20 : 1 × 20 5 4 2
= 4 : 5 : 10
or 4 men ≡ 5 women ≡ 10 children 4 men = 10 children
∴ 2 men ≡ 5 children and 6 men ≡ 15 children
5 women = 10 children
∴ 3 women ≡ 6 children
4 women ≡ 8 children
∴ 2 men + 3 women + 4 Children = 15 children
6 men + 4 women + 7 children = 30 children
where, x is no. of days
⇒ 30 × 10 × x = 15 × 16 × 10⇒ x = 15 × 16 × 10 = 8 days 30 × 10 Correct Option: D
Using Rule 1,
Ratio of the working capabilities of a man, a woman and a child = 5 : 4 : 2
∴ Ratio of man, woman and child equivalence= 1 : 1 : 1 5 4 2 = 1 × 20 : 1 × 20 : 1 × 20 5 4 2
= 4 : 5 : 10
or 4 men ≡ 5 women ≡ 10 children 4 men = 10 children
∴ 2 men ≡ 5 children and 6 men ≡ 15 children
5 women = 10 children
∴ 3 women ≡ 6 children
4 women ≡ 8 children
∴ 2 men + 3 women + 4 Children = 15 children
6 men + 4 women + 7 children = 30 children
where, x is no. of days
⇒ 30 × 10 × x = 15 × 16 × 10⇒ x = 15 × 16 × 10 = 8 days 30 × 10
