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P sells a cow to Q at a loss of 10% and ...

P sells a cow to Q at a loss of `10%` and Q sells it to R at a loss of `8%`. If R pays ₹1656 for it, at what price did P buy

A

₹1533

B

₹1803

C

₹1217

D

₹2000

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, let's break it down: ### Step 1: Understand the Selling Price from R to Q R pays ₹1656 for the cow. This is the selling price (SP) for Q. ### Step 2: Find the Cost Price for Q Q sells the cow to R at a loss of 8%. Therefore, if the selling price (SP) is ₹1656, we can find the cost price (CP) for Q using the formula: \[ SP = CP \times \left(1 - \frac{\text{Loss\%}}{100}\right) \] Here, Loss% = 8%. Thus, \[ 1656 = CP_Q \times \left(1 - \frac{8}{100}\right) \] \[ 1656 = CP_Q \times 0.92 \] Now, solving for CP_Q: \[ CP_Q = \frac{1656}{0.92} \] Calculating this gives: \[ CP_Q = 1800 \] ### Step 3: Find the Cost Price for P Now that we have the cost price for Q (which is ₹1800), we can find the cost price for P. P sells the cow to Q at a loss of 10%. Therefore, we can use the same formula: \[ SP = CP \times \left(1 - \frac{\text{Loss\%}}{100}\right) \] In this case, Loss% = 10%. Thus, \[ CP_Q = CP_P \times \left(1 - \frac{10}{100}\right) \] \[ 1800 = CP_P \times 0.90 \] Now, solving for CP_P: \[ CP_P = \frac{1800}{0.90} \] Calculating this gives: \[ CP_P = 2000 \] ### Conclusion Thus, the price at which P bought the cow is ₹2000.
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