P and Q started a business by investing a total of Rs. 9,600. If P invested for m months less than Q, then find the value of m given that P’s profit share is Rs. 2,400. Also, P invested Rs. 1,600 less than Q, and the total profit earned at the end of the year is Rs. 9,600.
Show answer & explanation
Correct answer: B
Explanation
Total Investment = ₹9600, Total Profit = ₹9600
P's Profit = ₹2400
P's Capital = x
Q's Capital = x + 1600
x + (x + 1600) = 9600
2x + 1600 = 9600
2x = 8000
x = 4000
P's Capital = 4000, Q's Capital = 5600
Profit Ratio = P : Q = 2400 : (9600 − 2400) = 2400 : 7200 = 1 : 3
4000(12 − m) : 5600(12) = 1 : 3
4000(12 − m) / (5600 × 12) = 1/3
(12 − m) / 12 = 1/3 × 5600 / 4000
(12 − m) / 12 = 7/15
12 − m = 12 × 7/15
12 − m = 84/15
m = 12 − 5.6 = 6.4 months