Question

Question:-
Arvind and Subu can paint a wall in 9 days. If Subu takes 15 days to paint it alone, how many days will Arvind
take to paint the wall?
Choices:-
45
12.5
22.5
25
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Answer 1

Answer :

Arvind takes 22.5 days to paint the wall alone.

Explanation :

Given :

• Arvind and Subu can paint a wall in 9 days.
• Subu takes 15 days to paint it alone

To find :

the number of days taken by Arvind to paint the wall

Solution :

 

Arvind and Subu together can paint the wall in 9 days.

The work done by them together in one day = 1/9

Subu takes 15 days to paint it alone.

The work done by Subu alone in one day = 1/15

Let Arvind alone takes x days to paint the wall.

The work done by Arvind alone in one day = 1/x

The work done by them together in one day =  The work done by Subu alone in one day +  The work done by Arvind alone in one day

    $\sf \dfrac{1}{9}=\dfrac{1}{15}+\dfrac{1}{x} \\\\ \sf \dfrac{1}{x}=\dfrac{1}{9}-\dfrac{1}{15} \\\\ \sf \dfrac{1}{x}= \bigg(\dfrac{1}{9}\times \dfrac{5}{5} \bigg) - \bigg(\dfrac{1}{15} \times \dfrac{3}{3} \bigg) \\\\ \sf \dfrac{1}{x}=\dfrac{5}{45}-\dfrac{3}{45} \\\\ \sf \dfrac{1}{x}=\dfrac{5-3}{45} \\\\ \sf \dfrac{1}{x}=\dfrac{2}{45} \\\\ \sf x=\dfrac{45}{2} \\\\ \sf x=22.5 \ days$

Therefore, Arvind takes 22.5 days to paint the wall alone.