P, Q started a business along with R. The initial investment of P is 20% less than the initial investment of Q. The ratio between the initial investments of P and R is 8:5 respectively. After ‘t’ months of the start of business, R left it. If at the end of ‘3t’ months, a total profit of Rs. 47200 was obtained, then find out the value of ‘t’.

Solution

The ratio between the initial investments of P and R is 8:5 respectively.

Let’s assume the initial investments of P and R is 8y and 5y respectively.

The initial investment of P is 20% less than the initial investment of Q.

8y = (100-20)% of initial investment of Q

8y = 80% of initial investment of Q

initial investment of Q = 10y

After ‘t’ months of the start of business, R left it.

Ratio among the investments  of P, Q and R with respect to the time = 8yxt+8yx2t : 10yxt+10yx2t : 5yxt

= 8+16 : 10+20 : 5

= 24 : 30 : 5

Here we cannot get the value of ‘t’ from the given information. So the answer cannot be determined.