5 kg sugar and 7 kg rice together cost ₹ 258, while 7 kg sugar and 5 kg rice together cost ₹ 246. Find the total cost of 8 kg sugar and 10 kg rice.

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

Given,

5 kg sugar and 7 kg rice together cost ₹ 258,

⇒ 5x + 7y = 258

⇒ 7y = 258 - 5x

⇒ y = $\dfrac{258 - 5x}{7}$     …..(1)

Given,

7 kg sugar and 5 kg rice together cost ₹ 246,

⇒ 7x + 5y = 246     …..(2)

Substituting value of y from equation (1) in (2), we get :

$\Rightarrow 7x + 5\Big(\dfrac{258 - 5x}{7}\Big) = 246 \\[1em] \Rightarrow \Big(\dfrac{49x + 1290 - 25x}{7}\Big) = 246 \\[1em] \Rightarrow 24x + 1290 = 246 \times 7 \\[1em] \Rightarrow 24x + 1290 = 1722 \\[1em] \Rightarrow 24x = 1722 - 1290 \\[1em] \Rightarrow x = \dfrac{432}{24} = 18.$

Substituting value of x in equation (1), we get :

$\Rightarrow y = \dfrac{258 - 5 \times 18}{7} \\[1em] \Rightarrow y = \dfrac{258 - 90}{7} \\[1em] \Rightarrow y = \dfrac{168}{7} \\[1em] \Rightarrow y = 24.$

Total cost of 8 kg sugar and 10 kg rice = 8x + 10y

= 8 × 18 + 10 × 24

= 144 + 240 = ₹ 384.

Hence, the total cost of 8 kg sugar and 10 kg rice = ₹ 384.