Question

Q and R went into a partnership for a year. The ratio between the initial investment of Q and R is 1 : 4. After 6 months, Q adds Rs.400 to his investment and after 5 months, R removes Rs.200 from his investment. The profit share of Q is Rs.1080. Total profit they had is Rs.2100. Find the initial investment of Q.
1. Rs.100
2. Rs.430
3. Rs.200
4. Rs.300
5. Rs.150

Answer 1

Correct Answer - Option 1 : Rs.100

Given:

Let the initial investment of Q and R be Rs.a and Rs.4a respectively.

⇒ Total investment of Q = a × 6 + (a + 400) × 6 = Rs.(12a + 2400)

⇒ Total investment of R = 4a × 5 + (4a - 200) × 7 = Rs.(48a - 1400)

⇒ Profit share of R = 2100 - 1080 = Rs.1020

Then,

⇒ (12a + 2400)/(48a - 1400) = 1080/1020

⇒ (12a + 2400)/(48a - 1400) = 36/34

⇒ (12a + 2400)/(48a - 1400) = 18/17

⇒ a = 100

∴ Initial investment of Q = Rs.100.