Time and Work
- A can complete a work in ‘m’ days and B can complete it in ‘n’ days. How many days will it take to complete the work if both A and B work together ?
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A’s 1 day’s work = 1 m B’s 1 day’s work = 1 n ∴ (A + B)’s 1 day’s work = 1 + 1 m n
Correct Option: D
A’s 1 day’s work = 1 m B’s 1 day’s work = 1 n ∴ (A + B)’s 1 day’s work = 1 + 1 m n (A + B)’s 1 day’s work = m + n = m + n mn mn ∴ Required time = mn m + n
- Three men A. B and C working together can do a job in 6 hours less time than A alone, in 1 hour less time than B alone and in one half the time needed by C when working alone. Then A and B together can do the job in
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Let A, B and C together do the work in t hours.
∴ Time taken by A = (d + 6) hours
Time taken by B = (t + 1) hours
Time taken by C = 2t hours∴ 1 + 1 + 1 = 1 t + 6 t + 1 2t t ⇒ 1 + 1 = 1 - 1 t + 6 t + 1 t 2t = 1 2t ⇒ 1 = 1 - 1 t + 6 2t t + 1 = t + 1 - 2t 2t(t + 1) = 1 = 1 - t t + 6 2t2 + 2t
⇒ 2t2 + 2t = t + 6 – t2 – 6t
⇒ 3t2 + 7t – 6 = 0
⇒ 3t2 + 9t – 2t – 6 = 0
⇒ 3t (t + 3) – 2 (t + 3) = 0
⇒ (3t – 2) (t +3) = 0
⇒ 3t – 2 = 0 as t + 3 ≠ 0
Correct Option: D
Let A, B and C together do the work in t hours.
∴ Time taken by A = (d + 6) hours
Time taken by B = (t + 1) hours
Time taken by C = 2t hours∴ 1 + 1 + 1 = 1 t + 6 t + 1 2t t ⇒ 1 + 1 = 1 - 1 t + 6 t + 1 t 2t = 1 2t ⇒ 1 = 1 - 1 t + 6 2t t + 1 = t + 1 - 2t 2t(t + 1) = 1 = 1 - t t + 6 2t2 + 2t
⇒ 2t2 + 2t = t + 6 – t2 – 6t
⇒ 3t2 + 7t – 6 = 0
⇒ 3t2 + 9t – 2t – 6 = 0
⇒ 3t (t + 3) – 2 (t + 3) = 0
⇒ (3t – 2) (t +3) = 0
⇒ 3t – 2 = 0 as t + 3 ≠ 0⇒ t = 2 3 ∴ Time taken by A = 6 + 2 3 = 18 + 2 = 20 hours 3 3 Time taken by B = 1 + 2 3 = 5 hours 3
∴ (A +B)’s 1 hour’s work= 3 + 3 20 5 = 3 + 12 20 = 15 = 3 20 4 ∴ Required time = 4 hours 3
- A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all the three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is
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Let Time taken by B and C = k days
∴ Time taken by A = 3k days∴ Part of work done by A, B and C in 1 day = 1 + 1 = 3 + 1 = 4 k 3k 3k 3k
∴ 4 = 1 ⇒ 3k = 4 × 24 3k 24
Correct Option: B
Let Time taken by B and C = k days
∴ Time taken by A = 3k days∴ Part of work done by A, B and C in 1 day = 1 + 1 = 3 + 1 = 4 k 3k 3k 3k
∴ 4 = 1 ⇒ 3k = 4 × 24 3k 24 ⇒ k = 4 × 24 = 32 days 3
∴ Time taken by A = 32 × 3 = 96 days
- A can do a piece of work in 4 days and B can do it in 12 days. In how many days will they finish the work, both working together ?
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A’s 1 day’s work = 1 4 B’s 1 day’s work = 1 12 (A + B)’s 1 day’s work = 1 + 1 4 12 (A + B)’s 1 day’s work = 4 = 1 12 3
∴ Required time = 3 days
Second method to solve this question ,
Correct Option: D
A’s 1 day’s work = 1 4 B’s 1 day’s work = 1 12 (A + B)’s 1 day’s work = 1 + 1 4 12 (A + B)’s 1 day’s work = 4 = 1 12 3
∴ Required time = 3 days
Second method to solve this question ,
Time taken = xy days x + y Time taken = 4 × 12 4 + 12 Time taken = 48 = 3 days 16
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A can do 1 of a work in 10 days. 4 B can do 1 of the work in 20 days. 3
In how many days can both A and B together do the work ?
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A does 1 work in 10 days 4
∴ A will do 1 work in 10 × 4 = 40 days
Similarly, B will do the same work in 20 × 3 = 60 days∴ (A + B)’s 1 day’s work = 1 + 1 40 60 = 3 + 2 120 (A + B)’s 1 day’s work = 5 = 1 120 24
∴ Required time = 24 days
Second method to solve this question ,
Time taken by A to finish the work = 40 days
Time taken by B to finish the work = 60 days
Correct Option: C
A does 1 work in 10 days 4
∴ A will do 1 work in 10 × 4 = 40 days
Similarly, B will do the same work in 20 × 3 = 60 days∴ (A + B)’s 1 day’s work = 1 + 1 40 60 = 3 + 2 120 (A + B)’s 1 day’s work = 5 = 1 120 24
∴ Required time = 24 days
Second method to solve this question ,
Time taken by A to finish the work = 40 days
Time taken by B to finish the work = 60 daysTotal time taken = x × y days x + y Total time taken = 40 × 60 40 + 60 Total time taken = 40 × 60 = 24 days 100
