3 pens and 5 pencils together cost ₹ 35, whereas 5 pens and 3 pencils together cost ₹ 37. The cost of a pencil is ………………

Monjur Alahi

3 pens and 5 pencils together cost ₹ 35, whereas 5 pens and 3 pencils together cost ₹ 37. The cost of a pencil is ………………

A) ₹ 5 

B) ₹ 3 

C) ₹ 4 

D) ₹ 6


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2 Answers

Salim Ahmed Kawsar

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Correct option is (C) ₹ 4

Let cost of 1 pen is Rs x and cost of 1 pencil is Rs y.

\(\because\) Cost of 3 pens & 5 pencils is Rs 35.

\(\therefore\) 3x + 5y = 35        __________(1)

\(\because\) Cost of 5 pens & 3 pencils is Rs 37.

\(\therefore\) 5x + 3y = 37        __________(2)

Multiply equation (1) by 5 and equation (2) by 3, we get

15x + 25y = 175      __________(3)

15x + 9y = 111        __________(4)

Subtract equation (4) from (3), we get

(15x + 25y) - (15x + 9y) = 175 - 111

\(\Rightarrow\) 25y - 9y = 64

\(\Rightarrow\) 16y = 64

\(\Rightarrow\) y = \(\frac{64}{16}\) = 4

\(\therefore\) Cost of a pencil is Rs 4.

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Salim Ahmed Kawsar

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Correct option is C) ₹ 4

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