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Question

5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the costs of one pencil and one pen.

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Solution

Let the cost of one pencil be x and that of one pen be y

5x+7y=50(i)

7x+5y=46(ii)

On multiplying eq.(i) by 5 and eq.(ii) by 7, we get

25x+35y=250(iii)

49x+35y=322(iv)

On subtracting eq.(iii) from (iv), we get

49x+35y(25x+35y)=322250

49x25x=72

24x=72

x=7224=3

On putting the value of x in eq.(i), we get

5×3+7y=50

7y=5015

y=357=5

Hence, the cost of one pencil is Rs. 3 and one pen costs Rs. 5


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