Question

the cost of 5 kg of sugar and 7 kg of rice is rupees 153 and the cost of 7 kg of sugar and 5kg of rice is rupees 147 find the cost of 6 kg of sugar and 10 kg of rice

Answer 1

let 1 kg sugar be x , and 1 kg rice be y

5x+7y = 153

7x + 5y = 147

12 x + 12y = 153 + 147

12x + 12y = 300

x + 12y = 300/12

x + 12 y = 25

x + y = 25/12

x+y = 2.5

price of 6 kg sugar and 10 kg rice = 2.5 * 6 * 10 = 150

Answer 2

Let’s assume the cost of 1 kg of sugar = Rs x

And, let the cost of 1 kg of rice = Rs y

Then according to the given conditions, we have

5x + 7y = 153 … (i) and

7x + 5y = 147 … (ii)

Multiplying (i) by 7 and (ii) by 5, we have

35x + 49y = 1071 … (iii)

35x + 25y = 735 … (iv)

(-)—(-)——(-)————- Subtracting (iv) from (iii), we get

24y = 336

y = 336/24

y = 14

On substituting the value of y in (i), we get

5x + 7(14) = 153

5x + 98 = 153

5x = 153 – 98

5x = 55

x = 55/5 = 11

So, the cost of 1 kg of sugar is Rs 11 and the cost of 1 kg of rice is Rs 14.

Now,

Cost of 6 kg of sugar = Rs 11 x 6 = Rs 66

Cost of 10 kg of rice = Rs 14 x 10 = Rs 140

Thus, the cost of 6 kg of sugar and 10 kg of rice = Rs 66 + Rs 140 = Rs 206.