Question

5 pencils and 7 pens together cost Rs. 50 whereas
7 pencils and 5 pens cost Rs. 46. The cost of 2
pencils and 3 pens is :
(1) Rs. 42
(2) Rs. 39
(3) Rs. 21
(4) Rs. 16
which is correct?​

Answer 1

Given:

• The cost of 5 pencils and 7 pens = Rs. 50
• The cost of 7 pencils and 5 pens = Rs. 46

To find:

• The cost of 2 pencils and 3 pens.

Solution:

» Let the cost of one pencil be x and cost of one pen be y.

ATQ,

• 5x + 7y = 50 ...[eq. 1]
• 7x + 5y = 46 ...[eq. 2]

By multiplying eq. 1 by 7, we get,

• 7(5x + 7y) = 7 × 50
• 35x + 49y = 350 ...[eq. 3]

And by multiplying eq. 2 by 5, we get,

• 5(7x + 5y) = 5 × 46
• 35x + 25y = 230 ...[eq. 4]

Subtracting eq. 4 from eq. 3,

⇒ 35x + 49y - 35x - 25y = 350 - 230

⇒ 24y = 120

⇒ y = 120/24

⇒ y = 5

Now, substituting value of y in eq. 1, we get,

⇒ 5x + 7 × 5 = 50

⇒ 5x + 35 = 50

⇒ 5x = 50 - 35

⇒ 5x = 15

⇒ x = 15/5

⇒ x = 3

Thus,

• Cost of one pencil = x = Rs. 3
• Cost of one pen = y = Rs. 5

Therefore,

• Cost of 2 pencils = 2x = 2 × 3 = Rs. 6
• Cost of 3 pens = 3y = 3 × 5 = Rs. 15
• Cost of 2 pencils and 3 pens together = Rs. (6 + 15) = Rs. 21

Hence, the cost of 2 pencils and 3 pens is Rs. 21. [option (3)]

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