Question

The cost of 5 kg of sugar and 7 kg of rice is 153 and the cost of 7 kg of sugar and > kg UI
is * 147. Find the cost of 7 kg of sugar and 11 kg of rice.
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Answer 1

Question:

The cost of 5 kg of sugar and 7 kg of rice is 153 and the cost of 7 kg of sugar and 5 kg of rice is 147. Find the cost of 7 kg of sugar and 11 kg of rice.

Step-by-step explanation:

Let the cost of 1kg of sugar and rice be x and y respectively.

So, 5 kg of sugar is 5x and 7 kg of rice is 7y.

And 7 kg of sugar is 7x and 5 kg of rice is 5y.

So, according to 1st equation,

5x + 7y = 153 -(1)

7x + 5y = 147 -(2)

Now, let's multiply the 1st equation by 5 and the 2nd equation by 7.

25x + 35y = 765 -(3)

49x + 35y = 1029 -(4)

Subtracting equation 1 by equation by 2.

24x = 264

x = 11

Putting x = 11 in equation 1

5 × (11) + 7y = 153

55 + 7y = 153

7y = 98

y = 14

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

So, price of 7 kg of sugar is 7 × (11) = 77

Price of 11 kg of rice is 11 × (14) = 154

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.