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I bought $5$ pens, $7$ pencils and $4$ erasers. Rajan bought $6$ pens, $8$ erasers and $14$ pencils for an amount which was half more than what I had paid. What percent of the total amount paid by me was paid for the pens?

1. $37.5$%
2. $625$%
3. $50$%
4. None of these

5 Pens + 7 Pencils + 4 erasers= Rs X ......(1)
6 Pens + 14 Pencils + 8 erasers= Rs Y ......bought by rajan
ATQ ( Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what I had paid.)

Y = 1.5X

6 Pens + 14 Pencils + 8 erasers= Rs 1.5X......(2)
Also, 10 Pens + 14 Pencils + 8 erasers= Rs 2X ( from 1).....(3)
(3) - (2) => 4 pen = 0.5X

1 pen = 0.125X

=> 5 pens=0.625X
percent of the total amount paid by me was paid for the pens = 0.625X/X *100=  62.5 %
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