Question

If A and B together finish a work in 15
days and B alone finish this work in 20
days, then in how many days will A alone
finish the work?
(a) 60 (b) 63
(c) 75 (d) 15​

Answer 1

Answer:-

$\red{\bigstar}$ Number of days A will take to finish the work

$\large\leadsto\boxed{\rm\green{60 \: days}}$

$\large\leadsto\boxed{\rm\pink{Option. A}}$

• Given:-

A and B together finish a work in 15 days.

B alone finishes the work in 20 days.

• To Find:-

Time taken by A to finish the work alone.

• Solution:-

✧ Time taken by A+B to complete the work = 15 days

Work of A+B in 1 day = 1/15

✧ Time taken by B to complete the work = 20 days

Work of B in 1 day = 1/20

✧ Time taken by A to complete the work = Time taken by [A+B] - Time taken by B

→ $\sf \dfrac{1}{15} - \dfrac{1}{20}$

Taking LCM:-

→ $\sf \dfrac{4 - 3}{60}$ $\: \: \: \: [\because LCM = 60]$

→ $\bf \dfrac{1}{60}$

Therefore, A will have to work for 60 days to finish the work.

Answer 2

Answer :-

• A → 60

Given :-

• A and B together finish a work in 15 days and B alone finish this work in 10 days

To Find :-

• In how many days will A alone finish this work ?

Solution :-

• Time taken by A + B to complete the work → 15 days

→ Work of A + B in one day → 1/15

• Time taken by B to complete the work → 20 days

→ Work of B in one day → 1/20

★ Time taken by A to complete the work = Time taken by A + B - Time taken by B

→ 1/15 - 1/20

→ 4 - 3/ 60

→ 1/60

Hence, A will take 60 days to complete the work alone.

Therefore option [A] is correct.