Question

A starts a business with an investment of
Rs 72000. After T months, B joined him
with an investment of Rs 60000. If at the
end of the year profit share of B is Rs 6500
out of total profit of Rs 25220, then find
the value of T.​

Answer 1

Given:

A starts a business with an investment of  Rs. 72000

After T months, B joined him with an investment of Rs. 60000

If at the  end of the year profit share of B is Rs 6500  out of the total profit of Rs. 25220

To find:

The value of T

Solution:

So,

The profit share of A is,

= [Total Profit] - [Profit share of B]

= Rs. 25200 - Rs. 6500

= Rs. 18700

Also, B has joined A after "T" months so, B's time of the investment in the business will be "12 - T" months.

We have the formula as:

$\boxed{\bold{Profit = Investment \times Time}}$

Therefore, we can say that,

$\frac{Profit\:of \:A}{Profit\:of\:B} = \frac{(Investment\:of\:A) \times (Time\: of\: investment\: of\: A)}{(Investment\:of\:B) \times (Time\: of\: investment\: of\: B)}$

on substituting the given values

$\frac{18700}{6500} = \frac{72000 \times 12}{60000 \times (12 - T)}$

$\implies 2.88 = \frac{72 \times 12}{60 \times (12 - T)}$

$\implies 2.88 = \frac{864}{720 - 60T}$

$\implies 2073.6 - 172.8T = 864$

$\implies 2073.6 - 864 = 172.8T$

$\implies 172.8T = 1209.6$

$\implies T = \frac{1209.6}{172.8}$

$\implies \bold{T = 7 \:months}$

Thus, the value of T is 7 months.

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