M and N started a business. M invested Rs. 69,000 more than N for 5 months, while N invested for 3 months. M's share is Rs. 720 more than that of N, out of a total profit of Rs. 2,160. Find the capital contributed by M.

Correct option is B

Given:

N invests x for 3 months.

M invests (x + 69000) for 5 months.

Total profit = Rs. 2,160; M’s share exceeds N’s by Rs. 720.

Formula Used:

Profit share $$\propto$$​ (Capital $$\times$$​ Time).

​Solution:​

From total and difference: if $$S_M+S_N =$$​ T and $$S_M-S_N$$​=D, then
​$$S_M=\frac{T+D}{2}; S_N=\frac{T-D}{2}$$​​

From 2: $$S_M=\frac{2160+720}{2}=1440, S_N=\frac{2160-720}{2}=720$$​​
So $$S_M : S_N = 1$$​440 : 720 = 2 : 1.

By 1: $$(x+69{,}000)\times 5 : x\times 3 = 2:1$$​​
​$$\dfrac{5(x+69{,}000)}{3x}=2$$​

5x+345000=6x

x=345000.

Hence M’s capital = x+69000 = 345000+69000 = Rs. 4,14,000