Question

The cost of 5 kg of sugar and 7 kg of
rice is Rs 153, and the cost of 7 kg
of sugar and 5 kg of rice is Rs. 47
Find the cost of 6 kg of sugar and 10kg
of rice​

Answer 1

Answer:

Make sugar = x

rice = y

5x + 7y = 153......Eq(1)

7x + 5y = 147......Eq(2)

Multiply Eq(1) by 5

Multiply Eq(2) by 7

25x + 35y = 765....Eq(1)

49x + 35y = 1029...Eq(2)

Subtract Eq(1) from Eq(2)

24x = 264

x = 11

Substitute x = 11 into Eq(1)

5x + 7y = 153......Eq(1)

5(11) + 7y = 153

55 + 7y = 153

7y = 153 - 55

7y = 98

y = 14

x = 11; y = 14

6kg of sugar

6(11) = 66

10kg of rice

10(14) = 140

Total price = 206

Hope this helps :-

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.