Ridhima and Minni embarked on a clothing house business with investments of Rs. (a-6000) and (2a-7000) respectively. After 8 months, Minni exited the business, and Cherry joined, contributing an investment of Rs. (a+4000). Meanwhile, Ridhima increased her investment by 50%. After an additional 6 months, both Ridhima and Cherry decreased their investments by Rs. 5000. Subsequently, Minni re-entered the business with an investment of Rs. (a+4000). At the end of two years, with a total profit of Rs. 50400 and Cherry's profit share being Rs. 12900, determine the percentage of (2a-7000) in relation to (a-6000).

Solution

ATQ, Ratio of investment with respect to the time for the investment of Ridhma, Minni and Cherry ⇒  (a-6000)x8+150% of (a-6000)x6+[150% of (a-6000)-5000]x10 : (2a-7000)x8+(a+4000)x10 : (a+4000)x6+[(a+4000)-5000]x10 At the end of two years, if there is a total profit of Rs. 50400 and the profit share of Cherry is Rs. 12900. [(a+4000)x6+[(a+4000)-5000]x10]/[(a-6000)x8+150% of (a-6000)x6+[150% of (a-6000)-5000]x10 + (2a-7000)x8+(a+4000)x10] = 12900/(50400-12900) [6a+24000+[a-1000]x10]/[(8a-48000)+1.5x(a-6000)x6+[1.5x(a-6000)-5000]x10 + (16a-56000)+10a+40000] = 12900/37500 [6a+24000 +10a -10000]/[(8a-48000)+9a-54000+[1.5a-9000-5000]x10+26a-16000] = 43/125 [16a+14000]/[(8a-48000)+9a-54000+[1.5a-14000]x10+26a-16000] = 43/125 [16a+14000]/[(8a-48000)+9a-54000+15a-140000+26a-16000] = 43/125 [16a+14000]/[58a-258000] = 43/125 After solving the above equation, a = 26000 Required % = [(2a-7000)/(a-6000)]x100 Put the value of ‘a’ in the above equation. = [(2x26000-7000)/(26000-6000)]x100 = [(52000-7000)/20000]x100 = [45000/20000]x100 = 45000/200 = 225%