Question

A and B together can do a piece of work in 10 days ,but A aline can do it in 15 days .how many days would b alone take to do the same work​

Answer 1

let B do work in x days

then he does 1/x work in 1 day

similarly, A does 1/15 work in 1 day

person | work | no. of days

A -> 1/15 -> 1

B -> 1/x -> 1

A and B -> 1/x + 1/15 ->1

so,

1/x + 1/15 = 1/10

1/x = 1/10 - 1/15

1/x = 1/30;

x = 30

hence B can finish 1 work in 30 days

Answer 2

Answer:

30 days.

Step-by-step explanation:

$\underline{\bigstar\:\textsf{Given:}}$

• A and B together can do work in 10 days.
• A alone can work in 15 days.

$\underline{\bigstar\:\textsf{To\:find:}}$

• In how many days B alone can do the same work = ?

$\underline{\bigstar\:\textsf{Solution:}}$

A can do a piece of work in 15 days.

So, work done by A in 1 day = 1/15.

Now, A + B = 10 days. So, work done by both in one day = 1/10

$\:\::\implies\:\sf{\dfrac{1}{15}\:+\:B\:=\:\dfrac{1}{10}}$

$\:$

$\:\::\implies\:\sf{B\:=\:\dfrac{1}{10}\:-\:\dfrac{1}{15}}$

$\:$

(Take L.C.M)

$\:$

$\:\::\implies\:\sf{B\:=\:\dfrac{15\:-\:10}{150}}$

$\:$

$\:\::\implies\:\sf{B\:=\:\dfrac{5}{150}}$

$\:$

$\:\::\implies\:\sf{B\:=\:\dfrac{1}{30}}$

$\:$

$\large\:\::\implies\underline{\boxed{\sf\purple{B\:can\:do\:same\:work\:in\:30\:days}}}$