Time and Work
- A and B together can complete a work in 8 days. B alone can complete that work in 12 days. B alone worked for four days. After that how long will A alone take to complete the work ?
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Time taken by A
= 8 × 12 = 8 × 12 = 24 days 128 4 Work done of by B = 4 = 1 12 3
Remaining work= 1 - 1 = 2 3 3
∵ A can complete a work in 24 days∴ A can complete 2 part of work in 24 × 2 = 16 days 3 3 Correct Option: C
Time taken by A
= 8 × 12 = 8 × 12 = 24 days 128 4 Work done of by B = 4 = 1 12 3
Remaining work= 1 - 1 = 2 3 3
∵ A can complete a work in 24 days∴ A can complete 2 part of work in 24 × 2 = 16 days 3 3
- A man and a boy can complete a work together in 24 days. If for the last six days man alone does the work then it is completed in 26 days. How long the boy will take to complete the work alone ?
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Suppose a man can complete the work in x days and that boys in y days.
According to question24 + 24 = 1 ......(i) × 13 x y 26 + 20 = 1 ......(ii) × 12 x y 312 + 312 = 13 x y 312 + 340 = 12 x y ⇒ 72 = 1 ⇒ y = 72 days y
∴ Boys alone can complete the work in 72 days
Aliter : Using Rule 9,
Here, a = 24, b = 24 – 6 = 18 d = 26 days
Total time taken by B alone to complete the work= bd - 6 a - b
( ∵ man has work d or 6 days)= 18 × 26 - 6 = 78 – 6 = 72 days 24 - 18 Correct Option: A
Suppose a man can complete the work in x days and that boys in y days.
According to question24 + 24 = 1 ......(i) × 13 x y 26 + 20 = 1 ......(ii) × 12 x y 312 + 312 = 13 x y 312 + 340 = 12 x y ⇒ 72 = 1 ⇒ y = 72 days y
∴ Boys alone can complete the work in 72 days
Aliter : Using Rule 9,
Here, a = 24, b = 24 – 6 = 18 d = 26 days
Total time taken by B alone to complete the work= bd - 6 a - b
( ∵ man has work d or 6 days)= 18 × 26 - 6 = 78 – 6 = 72 days 24 - 18
- A and B can do a work in 45 days and 40 days respectively. They began the work together but A left after some time and B completed the remaining work in 23 days. After how many days of the start of the work did A leave ?
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(A + B)’s 1 day’s work
= 
1 + 1 
= 17 45 40 360
Work done by B in 23 days= 1 × 23 = 23 40 40 Remaining work = 1 - 23 = 17 40 40 Now 17 work was done by (A + B) in 1 day 360 ∴ 17 work was done by 40 (A + B) in 1 × 360 × 17 = 9 days. 17 40
Hence, A left after 9 days.
Aliter : Using Rule 26,
Here, x = 45, y = 40, a = 23⇒ Required time t = (y - a) × x (x + y) t = (40 - 23) × 45 (45 + 40) = 17 × 45 = 9 days 85 Correct Option: B
(A + B)’s 1 day’s work
= 1 + 1 = 17 45 40 360
Work done by B in 23 days= 1 × 23 = 23 40 40 Remaining work = 1 - 23 = 17 40 40 Now 17 work was done by (A + B) in 1 day 360 ∴ 17 work was done by 40 (A + B) in 1 × 360 × 17 = 9 days. 17 40
Hence, A left after 9 days.
Aliter : Using Rule 26,
Here, x = 45, y = 40, a = 23⇒ Required time t = (y - a) × x (x + y) t = (40 - 23) × 45 (45 + 40) = 17 × 45 = 9 days 85
- 20 men can do a piece of work in 18 days, They worked together for 3 days, then 5 men joined them. In how many more days is the work completed ?
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Work done by 20 men in 3 days
= 3 = 1 part 18 6
Remaining work= 1 – 1 = 5 part 6 6 ∴ M1D1 = M2D2 W1 W2 ∴ 20 × 18 = 25 × D2 1 5/6
⇒ 6 × 25 × D2 = 5 × 20 × 18⇒ D2 = 5 × 20 × 18 = 12 days 6 × 25
Aliter : Using Rule 10,
Here, A = 20, a = 18 b = 3. B = 5
Required number of days= A(a - b) = 20 (18 - 3) A + B 20 + 5 = 20 × 15 = 12 days 25 Correct Option: B
Work done by 20 men in 3 days
= 3 = 1 part 18 6
Remaining work= 1 – 1 = 5 part 6 6 ∴ M1D1 = M2D2 W1 W2 ∴ 20 × 18 = 25 × D2 1 5/6
⇒ 6 × 25 × D2 = 5 × 20 × 18⇒ D2 = 5 × 20 × 18 = 12 days 6 × 25
Aliter : Using Rule 10,
Here, A = 20, a = 18 b = 3. B = 5
Required number of days= A(a - b) = 20 (18 - 3) A + B 20 + 5 = 20 × 15 = 12 days 25
- A can do a piece of work in 20 days and B in 15 days. With the help of C, they finish the work in 5 days. C can alone do the work in
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A’s 1 day’s work = 1 20 B’s 1 day’s work = 1 15 (A + B + C)’s 1 day’s work = 1 5 ∴ C’s 1 day’s work = 1 - 1 - 1 5 20 15 = 12 - 3 - 4 = 5 = 1 60 60 12
∴ Required time = 12 daysCorrect Option: D
A’s 1 day’s work = 1 20 B’s 1 day’s work = 1 15 (A + B + C)’s 1 day’s work = 1 5 ∴ C’s 1 day’s work = 1 - 1 - 1 5 20 15 = 12 - 3 - 4 = 5 = 1 60 60 12
∴ Required time = 12 days
