Question

8. Ram can do a piece of work in 12 days. Amir can do the same work in 6 days. If they work together,
in how many days will they finish the work?
a)6days
b)5days
c)4days
d)3days


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Answer 1

Answer is d) three days

Answer 2

Given

• Ram take time to complete a Work = 12 days
• Amir take time to complete a Work = 6 days.

Explanation:

One day Work of Ram will be ${\sf{ \dfrac{1}{12} }}$

One day Work of Amir will be ${\sf{ \dfrac{1}{6} }}$

Suppose that they Finish work together in x days as: ${\sf{ \dfrac{1}{x} }}$

Then, Both take time to complete work together as:-

$\maltese {\underline{\pmb{\sf{ According \ to \ Question : }}}} \\ \\ \\ \colon\implies{\sf{ \dfrac{1}{12} + \dfrac{1}{6} = \dfrac{1}{x} }} \\ \\ \\ \colon\implies{\sf{ \dfrac{1+2}{12} = \dfrac{1}{x} }} \\ \\ \\ \colon\implies{\sf{ \cancel{ \dfrac{3}{12} } = \dfrac{1}{x} }} \\ \\ \\ \colon\implies{\sf{ \dfrac{1}{4} = \dfrac{1}{x} }} \\ \\ \\ \colon\implies{\orange{\large{\pmb{\boxed{\sf{ x = 4 \ Days }}}}}}$

Hence,

$\\ {\underline{\sf{ They \ take \ 4 \ days \ to \ complete \ work. }}}$