Time and Work
- A can do a piece of work in 18 days. He worked at it for 12 days and B finished the remaining work in 8 days. B alone can do the whole work in
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∵ A’s 1 day’s work = 1 18 ∴ A’s 12 days’ work = 12 = 2 18 3
∴ Remaining work= 1 – 2 = 1 3 3 ∵ Time taken by B in doing 1 work = 8 days 3
∴ Time taken by B in doing whole work
= 3 × 8 = 24 daysCorrect Option: B
∵ A’s 1 day’s work = 1 18 ∴ A’s 12 days’ work = 12 = 2 18 3
∴ Remaining work= 1 – 2 = 1 3 3 ∵ Time taken by B in doing 1 work = 8 days 3
∴ Time taken by B in doing whole work
= 3 × 8 = 24 days
- A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
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(A + B)’s 1 day’s work
= 1 .......(i) 8
(B + C)’s 1 day’s work= 1 .......(ii) 12
(A + B + C)’s 1 day’s work= 1 .......(iii) 6
By equations (i) + (ii) – (iii),
B’s 1 day’s work⇒ 1 + 1 - 1 8 12 6 = 3 + 2 - 4 = 1 .........(iv) 24 24
By equations (iii) – (iv),
(A + C)’s 1 day’s work= 1 - 1 6 24 = 4 - 1 = 3 = 1 24 24 8
∴ Required time = 8 daysCorrect Option: C
(A + B)’s 1 day’s work
= 1 .......(i) 8
(B + C)’s 1 day’s work= 1 .......(ii) 12
(A + B + C)’s 1 day’s work= 1 .......(iii) 6
By equations (i) + (ii) – (iii),
B’s 1 day’s work⇒ 1 + 1 - 1 8 12 6 = 3 + 2 - 4 = 1 .........(iv) 24 24
By equations (iii) – (iv),
(A + C)’s 1 day’s work= 1 - 1 6 24 = 4 - 1 = 3 = 1 24 24 8
∴ Required time = 8 days
- A and B together can do a piece of work in 9 days. If A does thrice the work of B in a given time, the time A alone will take to finish the work is
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Let time taken by A be x days.
∴ Time taken by B = 3x days
According to the question,⇒ 1 + 1 = 1 x 3x 9 ⇒ 3 + 1 = 1 3x 9
⇒ 3x = 4 × 9⇒ x = 4 × 9 = 12 days 3 Correct Option: D
Let time taken by A be x days.
∴ Time taken by B = 3x days
According to the question,⇒ 1 + 1 = 1 x 3x 9 ⇒ 3 + 1 = 1 3x 9
⇒ 3x = 4 × 9⇒ x = 4 × 9 = 12 days 3
- If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?
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∴ 4 : 100 
: : 100 : x 100 : 4
⇒ 4 × 100 × x = 100 × 100 × 4⇒ x = 100 × 100 × 4 = 100 days 4 × 100 Correct Option: D
∴ 4 : 100 : : 100 : x 100 : 4
⇒ 4 × 100 × x = 100 × 100 × 4⇒ x = 100 × 100 × 4 = 100 days 4 × 100
- X can do a piece of work in ‘p’ days and Y can do the same work in ‘q’ days. Then the number of days in which X and Y can together do that work is
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X’s 1 day’s work = 1 p Y’s 1 day’s work = 1 q
(X + Y)’s 1 day’s work= 1 + 1 = p + q p q pq ∴ Required time = pq p + q Correct Option: C
X’s 1 day’s work = 1 p Y’s 1 day’s work = 1 q
(X + Y)’s 1 day’s work= 1 + 1 = p + q p q pq ∴ Required time = pq p + q
