Question

A can do a piece of work in 20 days and B in 25days. they began to work together . but A leaves after some days . B finish the remaining work in 11 days .after how many days did A leave​

Answer 1

Step-by-step explanation:

A's 1 day's work = 1/20

B's 1 days work = 1/25

Calculation:

(A + B)'s 1 day's work = (1/20 + 1/25) = 9/100

⇒ ( A + B)'s 5 day's work = (9/100 × 5) = 9/20

⇒ Remaining work = (1 - 9/20) = 11/20

∴ Remaining work is 11/20

Given:

Time taken by A to complete the work = 20 days

Time taken by B to complete the work = 25 days

Formula used:

Efficiency = Work/Time

Calculation:

LCM of 20 and 25 = 100 units = Total work

Efficiency of A = 100/20 units/day

⇒ 5 units/day

Efficiency of B = 100/25 units/day

⇒ 4 units/day

Efficiency of A and B together = (5 + 4) units/day

⇒ 9 units/day

Work done in 4 days = (9 × 5) units

⇒ 45 units

Work left = (100 - 45) units

⇒ 55 units

Required fraction = 55/100

⇒ 11/20

∴ Remaining work is 11/20