'P' and 'Q' started a partnership business with investment of Rs. 6000 and Rs. 9000 respectively. After 4 months, 'P' increased his investment by Rs. (y + 500) while 'Q' withdraws Rs. 'y' from his investment. If at the end of 1 year since starting the business, 'P' gets Rs. 4200 out of the total profit Rs. 9200, then find the value of 'y'.

Increased investment of 'P' = 6000 + (y + 500) = Rs. (6500 + y) Decreased investment of 'Q' = 9000 - y = Rs. (9000 - y) Respective ratio of profit shares of 'P' and 'Q' = {(6000 × 4) + (6500 + y) × 8}: {(9000 × 4) + (9000 - y) × 8} = (24000 + 52000 + 8y): (36000 + 72000 - 8y) = (76000 + 8y): (108000 - 8y) Profit share of 'Q' at the end of the year = 9200 – 4200 = Rs. 5000 So, ATQ; (76000 + 8y) / (108000 - 8y) = (4200/5000) = (21/25) 25 × (76000 + 8y) = 21 × (108000 - 8y) 1900000 + 200y = 2268000 - 168y 368y = 368000 So, 'y' = 368000 ÷ 368 = 1000