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Q.

37 pens and 53 pencils cost Rs.320, while 53 pens and 37 pencils cost Rs.400. Find the cost of a pen and a pencil.

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a

Pen= Rs 6.50, Pencil= Rs 1.50

b

Pen= Rs 6, Pencil= Rs 1

c

Pen= Rs 5, Pencil= Rs 1.50

d

Pen= Rs 6.50, Pencil= Rs 1

answer is A.

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Detailed Solution

Concept: Assume that a pencil costs x and a pen costs y, respectively. Multiply "a" by the price of one pen or pencil to get the cost of "a" pens or pencils. Create two-variable linear equations linking the price of pens and pencils. To get the price of a single pen and pencil, solve the equations using the elimination approach.
Let

x = cost of pen

and

y = cost of pencil

,
By the question,

Now adding the equation 1 and 2

Substituting the equation 1 and 2

Adding equation 3 and 4

Substituting the equation 5 in 3

Thus the cost of one pen Rs. 6.50 and one pencil is Rs. 1.50
Hence, the correct answer is option 1.

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