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Ashok purchased pens and pencils in the ratio \(2:3\) during his first visit and paid Rs. 86 to the shopkeeper. During his second visit, he purchased pens and pencils in the ratio \(4:1\) and paid…

Question and options

Ashok purchased pens and pencils in the ratio 2:32:3 during his first visit and paid Rs. 86 to the shopkeeper. During his second visit, he purchased pens and pencils in the ratio 4:14:1 and paid Rs. 112. The cost of a pen as well as a pencil in rupees is a positive integer. If Ashok purchased four pens during his second visit, then the amount he paid in rupees for the pens during the second visit is
  1. 100
  2. 25
  3. 112
  4. 12

Answer and explanation

Correct answer: A - 100

The four pens cost Rs. 100100. With pen price pp and pencil price qq, the second purchase gives 4p+q=1124p+q=112, so one first-visit bundle costs 2p+3q=56+52q>562p+3q=56+\frac52q>56. Two bundles would cost more than Rs. 8686, so 2p+3q=862p+3q=86, giving q=12q=12 and p=25p=25. Rs. 2525 is the price per pen, so multiply it by four.

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  • IPMAT Indore

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