B invests $500 more than A in business, but A’s investment in the business is for 4 months, whereas B’s investment is for 3 months only. If A’s share of total profit of $520 is $40 more than B’s. How much did A contribute to business?
The Usual Method
Let earning by A = a
Hence, earnings by B = 520 – a
Also, a – (520 – a) = 40
Ratio of Earnings = Ratio of Investment
Hence, 280 : 240 or 7 : 6 = Ratio of Investment
Let the amount invested by A be $x
Hence, amount invested by B = $(x + 500)
Thus, ratio of investments by A and B is
Estimated Time to arrive at the answer = 60 seconds.
First get the ratio of earnings of A and B by the usual method, i.e. 7 : 6.
The investment period of A is 4 months and 4 is not a factor of 7. The amount of investment has to be a factor of 7 so as to get 7 in the ratio. The only option which has a multiple of 7 is option ‘3’ $3500.
Estimated Time to arrive at the answer = 15 seconds.