Question

Antra and Manvi invested Rs 3780 and Rs 3960 in a business. After 3 months, Antra withdrew Rs 420 and Manvi withdrew Rs 180. At the same time Chetna joined them by investing Rs 4620. After a year, they made a profit of Rs 35,850. Find Manvi’s share in the annual profit.

Answer 1

Hint: First of all find the shares of Antra, Manvi and Chetna at the end of one year. The profit for Antra is multiplication of investment of Antra by 3 and it is given that after three months she withdrew Rs 420 so subtract 420 from 3780 and then multiply this result by 9. Similarly, calculate the share of Manvi. The share of Chetna is found by multiplying 4620 by 9 because she invested after 3 months so she will get profit for 9 months. Now, it is given that the total profit is Rs 35,850 so to find the Manvi’s share in annual profit divide the Manvi’s share by the total share of Antra, Manvi and Chetna and then multiply this result by 35,850.

Complete step-by-step answer:
First of all we will find the share of Antra, Manvi and Chetna at the end of the one year.
To find the share of Antra at the end of the one year first of all multiply the Antra’s investment by 3 and it is given that after 3 months she withdrew Rs 420 so subtract 420 from 3780 and then multiply this subtraction by 9. We have written the mathematical form of what we have just said.
 $ \begin{align}
  & Rs\left( 3780\times 3+3360\times 9 \right) \\
 & =Rs41580 \\
\end{align} $
Hence, Antra's share at the end of 1 year is Rs 41580.
The way we have calculated the share of Antra similarly we can find the share of Manvi too. By multiplying 3960 by 3 and then add this result with the multiplication of 3780 by 9.
 $ \begin{align}
  & Rs\left( 3960\times 3+3780\times 9 \right) \\
 & =Rs45900 \\
\end{align} $
Hence, the Manvi’s share at the end of 1 year is Rs 45900.
The share of Chetna is calculated by multiplying 4620 to 9. We have multiplied 4620 to 9 because Chetna has invested money after 3 months and we have to find the profit share at the end of one year so we subtracted 3 months from 12 months.
 $ \begin{align}
  & Rs\left( 4620\times 9 \right) \\
 & =Rs41580 \\
\end{align} $
Hence, the Chetna’s share at the end of 1 year is Rs 41580.
It is given that the total profit that these three girls have made is Rs 35,850.
Now, to find the annual profit share of Manvi we divide the share of Manvi that we have calculated above by the total share of Antra, Manvi and Chetna and then multiply the result of this division by 35850.
 $ \begin{align}
  & \left( \dfrac{45900}{41580+45900+41580} \right)\times 35850 \\
 & =\dfrac{45900}{129060}\times 35850 \\
 & =Rs12750 \\
\end{align} $
From the above calculation, we have got the Manvi’s share of annual profit is Rs 12750.

Note: In this problem, you are very prone to calculation mistakes so beware of it. You might have thought that why the Manvi’s share would not be Rs 45900. The answer is Rs 45900 is the total amount of Manvi at the end of 1 year according to her investment and here we are forgetting the total profit that has come from Antra, Manvi and Chetna. As we are asked to find the annual profit share so we have to take the ratio of Manvi’s amount by total amount and then multiply with total given profit.