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 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 __________.
Explanation:
Let the price of each pen and pencil be x and y respectively.
1st Visit: Let the number one pens and pencils bougth be 2a and 3a respentively. ⇒ 2a × x + 3a × y = 86 ...(1)
2nd Visit: Number of pens and pencils bougth are 4 and 1 respectively. ⇒ 4 × x + 1 × y = 112 ...(2)
(1) × 2 - (2) × a ⇒ 4ax + 6ay - (4ax + ay) = 172 - 112a ⇒ 5ay = 172 - 112a ⇒ y = (172 - 112a)/5a
Since a and y are positive integers, the only possible value of a = 1. ∴ y = 12
Substituting y = 12 in (2), we get x = 25.
∴ Amount he paid for pens during 2nd visit = 4x = Rs. 100
Hence, 100.
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