Four people P, Q, R and S started a business. The initial investment of P is Rs. 500 less than the initial investment of R. The ratio between the initial investment of Q and S is 6:5 respectively. The initial investment of R is 80% more than the initial investment of S. The initial investment of P is Rs. 4000. After six months of the start of business, P and R increased their investment by Rs. 500 and Q and S decreased their investment by Rs. 1000. At the end of one year, a total profit of Rs. 50000 was obtained from it. 13.6% of the annual profit obtained from the business was spent on donations and the remaining was distributed among them. Which of the following statements is/are true?

(i) The difference between the profit share of P and R is the square of an even number.

(ii) The profit share of S is Rs. 7200.

(iii) The sum of the profit share of R and Q is Rs. 24200.

Solution

The initial investment of P is Rs. 4000. The initial investment of P is Rs. 500 less than the initial investment of R. 4000 = initial investment of R - 500 initial investment of R = 4000+500 = Rs. 4500 The initial investment of R is 80% more than the initial investment of S. 4500 = (100+80)% of initial investment of S 180% of initial investment of S = 4500 1.8 x (initial investment of S) = 4500 initial investment of S = Rs. 2500 The ratio between the initial investment of Q and S is 6:5 respectively. initial investment of Q = (2500/5)x6 = Rs. 3000 After six months of the start of business, P and R increased their investment by Rs. 500 and Q and S decreased their investment by Rs. 1000. Ratio of the investment with respect to the time for P, Q, R and S = 4000x6+4500x6 : 3000x6+2000x6 : 4500x6+5000x6 : 2500x6+1500x6 = 4000+4500 : 3000+2000 : 4500+5000 : 2500+1500 = 8500 : 5000 : 9500 : 4000 = 17 : 10 : 19 : 8 At the end of one year, a total profit of Rs. 50000 was obtained from it. 13.6% of the annual profit obtained from the business was spent on donations and the remaining was distributed among them. Share of P, Q, R and S together = 50000 of (100-13.6)% = 50000 of 86.4% = 43200 Profit share of P = 43200 of [17/(17+10+19+8)] = 43200 x [17/54] = Rs. 13600 Profit share of Q = 43200 of [10/(17+10+19+8)] = 43200 x [10/54] = Rs. 8000 Profit share of R = 43200 of [19/(17+10+19+8)] = 43200 x [19/54] = Rs. 15200 Profit share of S = 43200 of [8/(17+10+19+8)] = 43200 x [8/54] = Rs. 6400 (i) The difference between the profit share of P and R is the square of an even number. difference between the profit share of P and R = 15200-13600 = 1600 The above given statement is true. (ii) The profit share of S is Rs. 7200. The above given statement is not true. (iii) The sum of the profit share of R and Q is Rs. 24200. sum of the profit share of R and Q = 15200+8000 = 23200 The above given statement is not true.