X sells a bicycle to Y at a profit of 30% and Y sells it to Z at a loss of 20%. If Z pays Rs. 520/= for it, at what price did X buy?
-
500
-
520
-
540
-
580
Working backwards: Z paid Rs. 520 after Y's 20% loss, so Y bought it for 520/0.8 = Rs. 650. X sold at 30% profit, so X's cost was 650/1.3 = Rs. 500. Verification: 500 + 30% of 500 (150) = 650; then 650 - 20% of 650 (130) = 520.
To find the price at which X bought the bicycle, we need to work backwards from the given information.
Let's assume the cost price of the bicycle for X is Rs. P.
X sells the bicycle to Y at a profit of 30%, so the selling price for Y would be P + 30% of P.
Y then sells the bicycle to Z at a loss of 20%, so the selling price for Z would be (P + 30% of P) - 20% of (P + 30% of P).
According to the given information, Z pays Rs. 520 for the bicycle. So, we can set up the equation:
(P + 30% of P) - 20% of (P + 30% of P) = 520
To solve this equation, let's simplify it step by step:
P + 0.3P - 0.2(P + 0.3P) = 520 P + 0.3P - 0.2P - 0.06P = 520 P + 0.3P - 0.2P - 0.06P = 520 1.1P - 0.26P = 520 0.84P = 520 P = 520/0.84 P ≈ 619.05
Therefore, the price at which X bought the bicycle is approximately Rs. 619.05.
Now, let's check the options to find the closest value to Rs. 619.05.
A. 500 - This option is incorrect because it is lower than the calculated value of Rs. 619.05. B. 520 - This option is incorrect because it is equal to the selling price for Z, not the buying price for X. C. 540 - This option is incorrect because it is higher than the calculated value of Rs. 619.05. D. 580 - This option is incorrect because it is higher than the calculated value of Rs. 619.05.
Therefore, the correct answer is A) 500, as it is the closest option to the calculated buying price of Rs. 619.05.