[62.5%] I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amoun

For Competitive Exams

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?

61.25%

61%

62.5%

60%

Explanation:

Assume P is the cost of one pen, C is cost of one Pencil & E is cost of one Eraser.

Let cost of 5 pens, 7 pencils and 4 erasers be X.

then, 5P + 7C + 4E = X ------------(i)

Rajan has bought 6 pens, 14 pencils and 8 erasers at 1.5x cost (half more than mine)

=> 6P + 14C + 8E = 1.5X ------------(ii)

Multiplying Equation 1 by 2 and subtracting 2nd equation from it:

10P + 14C + 8E = 2X

6P + 14C + 8E = 1.5X

----------------------------

4P = 0.5X

=> P = 0.5X/4

Total amount paid by me for pens = 5P= 0.5X/4 $\times$ 5 = 2.5X/4

Percent of the total amount paid by me for the pens = {(2.5X/4)/X} $\times$ 100 = 62.5%.

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