Question

7. A multinational company placed orders for printing papers and writing pads. In the first order 5 carton of printing papers and 10 writing pads were ordered and total cost was Rs. 3000 and in the second order 10 carton of printing papers and 5 writing pads were ordered and total cost was Rs. 5250. What was the cost of one carton of printing paper and one writing pad?

Answer 1

Given:

In the first order 5 carton of printing papers and 10 writing pads were ordered and total cost was Rs. 3000.

In the second order 10 carton of printing papers and 5 writing pads were ordered and total cost was Rs. 5250.

To find:

The cost of one carton of printing paper and one writing pad

Solution:

Let's assume

"x" → cost of one carton of printing paper

"y" → cost of one writing pad

According to the question, we can form the following linear equations as,

1st order → 5x + 10y = 3000 ...... (i)

2nd order → 10x + 5y = 5250 ...... (ii)

We will multiply eq. (i) by 10 and eq. (ii) by 5

5x + 10y = 3000 ] × 10

⇒ 50x + 100y = 30000 ...... (iii)

and

10x + 5y = 5250 ] × 5

⇒ 50x + 25y = 26250 ...... (iv)

Subtracting eq. (iv) from (iii), we get

50x + 100y = 30000

50x + 25y = 26250

-      -             -

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

    75y = 3750

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∴ y = 50 ← price of one writing pad

Substituting the value of y = 50 in eq. (i), we get

5x + 10y = 3000

⇒ 5x + (10 × 50) = 3000

⇒ 5x + 500 = 3000

⇒ 5x = 3000 - 500

⇒ 5x = 2500

⇒ x = $\frac{2500}{5}$

⇒ x = 500 ← price of one carton of printing paper

Thus, $\boxed{\bold{The \:cost\: of\: one\: carton\: of\: printing \:paper\: is\:Rs.\:500\:and\: one\: writing\: pad\:is\:Rs.\:50.}}$

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