IPMAT Question Paper 2020 | IPM Indore Quants

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Question 6 : 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. I 12 . 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 __________.

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Video Explanation

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Explanatory Answer

Ratio of pen : pencil is 2:3 and he spends Rs 86
Next time The ratio of pen and pencil is 4:1 and he spends Rs 112
Second time Ashok purchased 4 pens, So the ratio of Pen and Pencil is 4:1
Hence he purchased 4 pens and 1 pencil during his second visit
Let price of pen be 'x' and price of pencil be 'y'
Then,
4x + y = 112. -----(2)
2x + 3y = 86 -----(1)----(From first visit)

(1) Is in Ratios, so it can be 4x + 6y = 86 (or)
6x + 9y = 86 (or)
8x + 12y = 86

Since, From (2), 4 pen and a pencil costs Rs 112
4 pens and 6 pencils has too cost more than 112 (Given that Cost of a pen and pencil is a positive integer)

In that case 4x + 6y = 86 (or)
6x + 9y = 86 (or)
8x + 12y = 86
These possibilities are ruled out

Only possibility is 2x + 3y = 86

Solving (1) and (2) by Elimination Method

We get y = 12 ---> Cost of a pen
On second visit, he pays a total of Rs 112, One pencil and 4 pen.
1 Pencil costs Rs 12, 112 - 12 = Rs 100

He paid Rs 100 during his second visit for the pens.

The answer is 100

 

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