'X' and 'Y' started a business by investing Rs.(p + 400) and Rs.(2p - 800), respectively. If at the end of the year, profit share of 'X' was Rs.18,000 out of total profit of Rs.42,000, then find the amount invested by 'Y'

ATQ, Let the amount invested by X be (p + 400) and the amount invested by Y be (2p - 800). Total profit = Rs. 42,000 X's profit share = Rs. 18,000 So, Y's profit share = Total profit - X's profit share Y's profit share = Rs. 42,000 - Rs. 18,000 Y's profit share = Rs. 24,000 Now, we know that profit is distributed in proportion to the amount invested. Therefore, we can set up the following equation: (X's investment) / (Y's investment) = (X's profit share) / (Y's profit share) Substitute the values: [(p + 400)] / [(2p - 800)] = 18,000 / 24,000 (p + 400) / (2p - 800) = 3/4 4(p + 400) = 3(2p - 800) 4p + 1600 = 6p - 2400 1600 = 2p - 2400 2p = 4000 p = 2000 Now that we have found the value of p, we can find the amount invested by Y: Y's investment = 2p - 800 Y's investment = 2(2000) - 800 Y's investment = 4000 - 800 Y's investment = Rs. 3200 So, the amount invested by Y is Rs. 3200.