Question:

P sells a table to Q at a profit of 10% and Q sells it to R at a profit of 12%. If R pays Rs. 246.40 for it, then how much had P paid for it?

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Two successive profits multiply, they do not add. Divide 246.40 by 1.12 to get what Q paid, then divide that by 1.10 to get what P paid.
Updated On: Jul 17, 2026
  • 200.00
  • 300.00
  • 248.00
  • 346.00
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The Correct Option is A

Solution and Explanation

Step 1: Set up what each sale does to the price.
Let the amount P paid for the table be \( x \) rupees. That is the cost price at the very start of the chain.
When someone sells at a profit of \( p\% \), the selling price is the cost price multiplied by \( \left(1+\frac{p}{100}\right) \). This is the rule the whole question rests on, so each sale simply multiplies the price by a fixed factor.

Step 2: Find the price Q pays.
P sells to Q at 10 per cent profit, so Q pays
\[ x \times \left(1+\frac{10}{100}\right) = 1.10x \]

Step 3: Find the price R pays.
For Q, the cost price is \( 1.10x \). Q sells to R at 12 per cent profit, so R pays
\[ 1.10x \times \left(1+\frac{12}{100}\right) = 1.10x \times 1.12 = 1.232x \]
So the two profits together multiply P's cost by \( 1.232 \). Note that this is not the same as a single 22 per cent profit, because Q's profit is worked out on the raised price, not on the original one.

Step 4: Use the given amount and solve.
R actually paid Rs. 246.40, so
\[ 1.232x = 246.40 \]
\[ x = \frac{246.40}{1.232} = 200 \]
To see the division clearly, multiply top and bottom by 1000: \( \frac{246400}{1232} = 200 \).

Step 5: Check the answer and the wrong options.
Start with 200. Add 10 per cent: \( 200 + 20 = 220 \), which is what Q pays. Add 12 per cent of 220: \( 220 + 26.40 = 246.40 \), which matches the given figure exactly.
Option (C) 248 comes from treating the profits as a flat 22 per cent and dividing 246.40 by 1.22 roughly, or from careless rounding.
Option (B) 300 and option (D) 346 are both larger than or close to what R paid, which is impossible, since the price only goes up along the chain and P must have paid less than R.

Final Answer:
P originally paid Rs. 200 for the table.
\[ \boxed{\text{Rs. }200} \]
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