Question

A book seller sold a box of 10 pencils for Rs. 80 and incurred a loss. Had he sold it for Rs. 98, his gain would have been twice the loss he incurred earlier. The cost price of the box of pencils is:

• A. Rs. 84
• B. Rs. 86
• C. Rs. 88
• D. Rs. 90

Hint:

When "gain is twice the loss", set up the equation using CP–SP relationships directly.

Answer 1

The Correct Option is B

Step 1: Rs. 80 is below the cost price by the loss amount, and Rs. 98 is above the cost price by the gain amount.

Step 2: The gap between Rs. 98 and Rs. 80 covers the loss and the gain together, so \( 98 - 80 = \text{loss} + \text{gain} \). Since the gain is twice the loss, this gap equals \( \text{loss} + 2 \times \text{loss} = 3 \times \text{loss} \).

Step 3: So \( 3 \times \text{loss} = 18 \), which gives \( \text{loss} = 6 \). The cost price is \( 80 + 6 = 86 \).
\[ \boxed{86} \]

Answer 2

Since the gain from selling at Rs. 98 must be exactly twice the loss from selling at Rs. 80, the cost price can be found directly as a weighted average of the two selling prices, weighting Rs. 80 twice as heavily as Rs. 98 (in a 2:1 ratio). We can apply this weighted average and check it against each option.

1. Rs. 84: The weighted average \( \frac{2 \times 80 + 1 \times 98}{3} = \frac{160+98}{3} = 86 \) does not equal 84, so this option is ruled out.
2. Rs. 86: The weighted average \( \frac{2 \times 80 + 1 \times 98}{3} = \frac{258}{3} = 86 \) matches this option exactly.
3. Rs. 88: The weighted average computed above is 86, not 88, so this option does not fit.
4. Rs. 90: The weighted average is 86, not 90, so this option is also ruled out.

Weighting Rs. 80 twice as heavily as Rs. 98, in line with the loss being half the gain, gives a cost price of exactly Rs. 86.

Therefore, the correct answer is Rs. 86.