Question

A can do a piece of work in 14days while B can do it 21days they began together worked for 7days ,then A fell ill and B had to complete the work in how many days was work completed? Ans -7/2

​

Answer 1

Answer:-

Given:

Amount of work completed by A in 14 days = 1

⟹ Amount of work completed by A in 1 day = 1/14

Amount of work completed by B in 21 days = 1

⟹ Amount of work completed by B in 1 day = 1/21.

Also,

They together completed a certain part of the work in 7 days.

⟶ Work completed by both A & B in 7 days = 1 - x

⟶ Work completed by both A and B in 1 day = (1 - x)/7

According to the question,

⟹ 1/14 + 1/21 = (1 - x) / 7

⟹ (3 + 2) / 42 = (1 - x) / 7

⟹ 5/42 = (1 - x) / 7

⟹ 5 × 7 = 42 (1 - x)

⟹ 5 × 7 / 42 = 1 - x

⟹ 5/6 = 1 - x

⟹ x = 1 - 5/6

⟹ x = (6 - 5) / 6

⟹ x = 1/6

Hence,

• Amount of work done by B in n days = 1/6

[ Let the number of days b completes be n ]

⟹ Amount of work done by B in 1 day = (1/6) / n = 1/6n.

So,

⟹ 1/21 = 1/6n

⟹ 6n = 21

⟹ n = 21/6

⟹ n = 7/2 days.

Hence,

• B takes 7/2 days to complete the remaining part of the work.

Now,

Total number of days required to complete the work = 7 + 7/2

⟶ (14 + 7) / 2 = 21/2 days.

∴ The work will be completed in 21/2 days.