X and Y started a business by investing Rs. 9.84 lakhs in the ratio 21 ∶ 20. After 5 months, X increased his investment by Rs. 2.96 lakhs. After a month, Z joined the business by investing Rs. 10 lakhs. After another month, Y sold 50% of his share to Z, while X increased his investment by Rs. 2 lakhs. At the end of the year, what part of the profit share will Z receive?

X and Y started a business by investing Rs. 9.84 lakhs in the ratio 21 ∶ 20. After 5 months, X increased his investment by Rs. 2.96 lakhs. After a month, Z joined the business by investing Rs. 10 lakhs. After another month, Y sold 50% of his share to Z, while X increased his investment by Rs. 2 lakhs. At the end of the year, what part of the profit share will Z receive? Correct Answer 10/29

Calculation:

X and Y initially invested Rs. 9.84 lakhs in ratio 21∶ 20

⇒ X’s initial investment = (21/41) × 9.84 = Rs. 5.04 lakhs

⇒ Y’s initial investment = 9.84 - 5.04 = Rs. 4.8 lakhs

Now,

X increased his investment by Rs. 2.96 lakhs after 5 months & by Rs. 2 lakhs after 1 + 1 = 2 more months,

⇒ X’s actual investment = (5.04 × 5) + + = 25.2 + 16 + 50 = 91.2

Y sold 50% of his share to Z after 5 + 1 + 1 = 7 months,

⇒ Y’s actual investment = (4.8 × 7) + (0.5 × 4.8 × 5) = 33.6 + 12 = 45.6

Z invested Rs. 10 lakhs after 5 + 1 = 6 months, & bought 50% share of Y after 1 more month, 

⇒ Z’s actual investment = (10 × 1) +  × 5 = 10 + 62 = 72

∵ Ratio of profit shares = Ratio of actual investments 

⇒ Ratio of profit shares of X, Y & Z = 91.2 ∶ 45.6 ∶ 72 = 38 ∶ 19 ∶ 30 

Sum of ratios = 38 + 19 + 30 = 87