'P' and 'Q' started a business by investing Rs. 20,800 and Rs. 16,000, respectively. After 'T' months later, 'R' joined them by investing 25% more than 'P'. If at the end of 1.5 years, the ratio of profit shares of 'Q', and 'R' is 12:13, respectively, then find the value of 'T'.

Correct option is B

Given:
Investment of P = 20800
Investment of Q = 16000
R joins after T months with 25% more investment than P.
Total time = 1.5 years = 18 months
Ratio of profit shares of Q and R = 12:13
Formula Used:
Profit Ratio = Investment × Time Period
Solution:
Investment of R = 20800 + 25% of 20800
Investment of R = 20800 × 1.25 = 26000
Time period for Q = 18 months
Time period for R = 18 - T months
Profit share ratio of Q to R:
$$\frac{16000 × 18}{26000 × (18 - T)}$$​ = $$\frac{12}{13}$$​​
​$$\frac{288000}{26000 × (18 - T)} = \frac{12}{13}$$​​
​$$\frac{144}{13 × (18 - T)} = \frac{12}{13}$$​​
144 = 12 × (18 - T)
12 = 18 - T
T = 6
Final Answer
So the correct answer is (b)