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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: X and Y started a partnership business by investing in the ratio 5 ∶ 6. Z joined them after 4 months with an amount equal to 2/3rd of that of Y. What was their total profit at the end of the year, if Z got Rs. 28000 as his share? Quantity B: Two friends P and Q started a business investing amount in the ratio of 5 : 6. R joined them after 6 months investing an amount equal to that of Q’s amount. At the end of year 20% profit was earned which was equal to Rs. 98,000. What was the amount invested by R?

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: X and Y started a partnership business by investing in the ratio 5 ∶ 6. Z joined them after 4 months with an amount equal to 2/3rd of that of Y. What was their total profit at the end of the year, if Z got Rs. 28000 as his share? Quantity B: Two friends P and Q started a business investing amount in the ratio of 5 : 6. R joined them after 6 months investing an amount equal to that of Q’s amount. At the end of year 20% profit was earned which was equal to Rs. 98,000. What was the amount invested by R? Correct Answer Quantity A < Quantity B

Quantity A: 

Let the investment by X = 5x and Investment by Y = 6x

∴ Investment by Z = 6x × 2/3 = 4x

The ratio in which the profit would be shared = (5x × 12) ∶ (6x × 12) ∶ (4x × 8) = 15 ∶ 18 ∶ 8

Since the share of Z = Rs. 28000

∴ 8/41 × (Total profit) = 28000

⇒ Total profit = Rs. 143500

Quantity B:

20% of Profit = 98000

Total profit = 98000 × 100/20 = 490000

Let amount invested by R be Rs.R.

Given,

P : Q = 5 : 6

Investment of P = 5A

Investment of Q = 6A

Annual investment of P and Q = 60A and 72A

Investment of R = 6A × 6 = 36A

Then,

⇒ 60A + 72A + 36A = 490000 × 12

⇒ 168A = 490000 × 12

⇒ A = 35000

∴ R’s investment = 35000 × 6 = Rs.210000

∴ Quantity A < Quantity B

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