Question:medium

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:

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

Step 1: Set up the cost price as an unknown.
Let the cost price of the box of pencils be \( x \). Since selling at Rs. 80 gives a loss, \( x > 80 \), and the loss is \( x - 80 \).

Step 2: Express the gain at the higher selling price.
Selling at Rs. 98 gives a gain of \( 98 - x \).

Step 3: Apply the condition and solve.
The gain is twice the loss: \[ 98 - x = 2(x-80) \] \[ 98 - x = 2x - 160 \] \[ 258 = 3x \] \[ x = 86 \]

Step 4: Final Answer.
Checking back, loss at Rs. 80 is Rs. 6 and gain at Rs. 98 is Rs. 12, which is exactly twice the loss. \[ \boxed{x = \text{Rs. } 86} \]
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Approach Solution -2

Since the gain at Rs. 98 must come out to exactly twice the loss at Rs. 80, checking each option is a matter of testing whether the quantity "gain minus twice the loss" equals zero for that cost price.

  1. Rs. 84: Loss at Rs. 80 is \( 84-80=4 \), and gain at Rs. 98 is \( 98-84=14 \). Testing the condition, \( 14 - 2(4) = 14-8=6 \), which is not zero, so this cost price fails the check.
  2. Rs. 86: Loss at Rs. 80 is \( 86-80=6 \), and gain at Rs. 98 is \( 98-86=12 \). Testing the condition, \( 12-2(6)=12-12=0 \), exactly satisfying the required relationship.
  3. Rs. 88: Loss is \( 88-80=8 \), and gain is \( 98-88=10 \). Testing the condition, \( 10-2(8)=10-16=-6 \), not zero, so this fails.
  4. Rs. 90: Loss is \( 90-80=10 \), and gain is \( 98-90=8 \). Testing the condition, \( 8-2(10)=8-20=-12 \), far from zero, ruling this out as well.

Only a cost price of Rs. 86 makes the gain-minus-twice-loss check land exactly on zero, satisfying the condition described in the question.

Therefore, the correct answer is Rs. 86.

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