The cost of 5 kg of sugar and 7 kg of rice is ₹765 and the cost of 7 kg of sugar and 5 kg of rice is ₹735. Find the cost of 6 kg of sugar and 10 kg of rice.

Let cost of sugar and rice per kg be ₹ x and ₹ y respectively.

So, cost of 5 kg of sugar and 7 kg of rice = 5x + 7y and,

cost of 7 kg of sugar and 5 kg of rice = 7x + 5y.

Given,

Cost of 5 kg of sugar and 7 kg of rice is ₹ 765.

⇒ 5x + 7y = 765 …………………(1)

Cost of 7 kg of sugar and 5 kg of rice is ₹ 735

⇒ 7x + 5y = 735 …………………(2)

Multiplying eq (1) by 7, we get :

⇒ 7(5x + 7y) = 7 × 765

⇒ 35x + 49y = 5355 …………………(3)

Multiplying eq (2) by 5, we get :

⇒ 5(7x + 5y) = 5 × 735

⇒ 35x + 25y = 3675 …………………(4)

Subtracting equation (4) from (3) we get,

⇒ 35x + 49y - (35x + 25y) = 5355 - 3675

⇒ 35x - 35x + 49y - 25y = 5355 - 3675

⇒ 24y = 1680

⇒ y = $\dfrac{1680}{24}$

⇒ y = 70.

Substituting the value of y in (1) we get,

⇒ 5x + 7(70) = 765

⇒ 5x + 490 = 765

⇒ 5x = 765 - 490

⇒ 5x = 275

⇒ x = $\dfrac{275}{5}$

⇒ x = 55.

∴ Cost of 6 kg of sugar and 10 kg of rice = 6x + 10y

= 6(55) + 10(70) = 330 + 700 = ₹ 1,030.

Hence, cost of 6kg of sugar and 10 kg of rice = ₹ 1,030.