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Given below are two quantities. Based on the given information, you have to determine the relation between the two quantities. Quantity A: P, Q and R can complete a piece of work alone in 10, 15 and 20 days respectively. They started together but P left after some days due to which the wages paid to P and R are same. If the work lasts 6 days, find after how many days P left. Quantity B: The sum and difference of wages of X and Y is Rs. 1120 and Rs. 160. Find the number of days in which X will complete the work alone if Y alone does it in 4 days. 

Given below are two quantities. Based on the given information, you have to determine the relation between the two quantities. Quantity A: P, Q and R can complete a piece of work alone in 10, 15 and 20 days respectively. They started together but P left after some days due to which the wages paid to P and R are same. If the work lasts 6 days, find after how many days P left. Quantity B: The sum and difference of wages of X and Y is Rs. 1120 and Rs. 160. Find the number of days in which X will complete the work alone if Y alone does it in 4 days.  Correct Answer Quantity A = Quantity B or No relation

Quantity A:

P, Q and R can complete a piece of work alone in 10, 15 and 20 days respectively

Suppose the total work is 60 (LCM of 10, 15 and 20)

⇒ Efficiency of P = 60/10 = 6

⇒ Efficiency of Q = 60/15 = 4

⇒ Efficiency of R = 60/20 = 3

As, the work lasts 6 days and P left after some days due to which the wages paid to P and R are same, so work of P and R will be equal

⇒ Work of R = (Number of days of work) × Efficiency = 6 × 3 = 18

⇒ Work of P = Work of R = 18

⇒ Number of days of work of P = 18/6 = 3 days

So, P left after 3 days

Quantity B:

The sum and difference of wages of X and Y is Rs. 1120 and Rs. 160

⇒ X + Y = 1120

⇒ X - Y = 160

⇒ X = 640 and Y = 480

⇒ Ratio of wages of X and Y = 640 ∶ 480 = 4 ∶ 3

Wages will be proportional to efficiency and time taken will be indirectly proportional to efficiency.

⇒ Ratio of time taken by X and Y = 3 ∶ 4

As, Y completes the work in 4 days, X will complete it in 3 days

∴ Quantity A = Quantity B

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