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 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:
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When "gain is twice the loss", set up the equation using CP–SP relationships directly.
Updated On: Jul 15, 2026
- Rs. 84
- Rs. 86
- Rs. 88
- Rs. 90
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The Correct Option is B
Approach Solution - 1
Let the cost price be Rs. $x$.
Loss in first case: $x - 80$.
Gain in second case: $98 - x$.
Given: Gain = 2 × Loss
$98 - x = 2(x - 80)$
$98 - x = 2x - 160$
$98 + 160 = 3x$
$258 = 3x$
$x = 86$ Rs.
Loss in first case: $x - 80$.
Gain in second case: $98 - x$.
Given: Gain = 2 × Loss
$98 - x = 2(x - 80)$
$98 - x = 2x - 160$
$98 + 160 = 3x$
$258 = 3x$
$x = 86$ Rs.
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Approach Solution -2
The question asks for the cost price of a box of pencils, given that selling it for Rs. 80 caused a loss, while selling it for Rs. 98 would have given a gain exactly twice that loss. Instead of setting up an equation, we can test each option directly by checking whether it satisfies "gain equals twice the loss."
- Rs. 84: Loss at Rs. 80 is \( 84 - 80 = 4 \). Gain at Rs. 98 is \( 98 - 84 = 14 \). Twice the loss is \( 2 \times 4 = 8 \), which does not equal 14, so this cost price does not fit.
- Rs. 86: Loss at Rs. 80 is \( 86 - 80 = 6 \). Gain at Rs. 98 is \( 98 - 86 = 12 \). Twice the loss is \( 2 \times 6 = 12 \), which exactly matches the gain, so this cost price fits.
- Rs. 88: Loss at Rs. 80 is \( 88 - 80 = 8 \). Gain at Rs. 98 is \( 98 - 88 = 10 \). Twice the loss is \( 2 \times 8 = 16 \), which does not equal 10, so this cost price does not fit.
- Rs. 90: Loss at Rs. 80 is \( 90 - 80 = 10 \). Gain at Rs. 98 is \( 98 - 90 = 8 \). Twice the loss is \( 2 \times 10 = 20 \), which does not equal 8, so this cost price does not fit.
Only Rs. 86 satisfies the condition that the gain on selling at Rs. 98 is exactly twice the loss on selling at Rs. 80.
Therefore, the correct answer is Rs. 86.
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Approach Solution -3
The book seller's cost price must sit between Rs. 80 and Rs. 98 in a very particular way: the gap above Rs. 80 (the loss) and the gap below Rs. 98 (the gain) must split in a 1:2 ratio, since the gain is twice the loss. We can test each option by checking whether it splits the Rs. 80-to-Rs. 98 span in exactly that ratio.
- Rs. 84: This is \( 84-80=4 \) above Rs. 80 and \( 98-84=14 \) below Rs. 98, a split of \( 4:14 \), which reduces to \( 2:7 \), not \( 1:2 \).
- Rs. 86: This is \( 86-80=6 \) above Rs. 80 and \( 98-86=12 \) below Rs. 98, a split of \( 6:12 \), which reduces exactly to \( 1:2 \).
- Rs. 88: This is \( 88-80=8 \) above Rs. 80 and \( 98-88=10 \) below Rs. 98, a split of \( 8:10 \), which reduces to \( 4:5 \), not \( 1:2 \).
- Rs. 90: This is \( 90-80=10 \) above Rs. 80 and \( 98-90=8 \) below Rs. 98, a split of \( 10:8 \), which reduces to \( 5:4 \), not \( 1:2 \).
Only Rs. 86 divides the Rs. 80-to-Rs. 98 span in the 1:2 ratio that a loss-to-gain ratio of 1:2 requires.
Therefore, the correct answer is Rs. 86.
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