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The ratio of price of rice per kg in shops A, B and C is 10 ∶ 14 ∶ 19 and the ratio of the price of wheat per kg in shops A, B and C is 5 ∶ 8 ∶ 9 respectively. If the ratio of price of (3 kg rice + 2 kg wheat from shop A), (5 kg rice and 7 kg of wheat from shop B) and (5 kg rice from shop C and Rs. 135 worth other materials from shop B) is 2 ∶ 7 ∶ 6. What is the price of 25 kg of rice from shop A and 15 kg of wheat of shop B? (in rupees)

The ratio of price of rice per kg in shops A, B and C is 10 ∶ 14 ∶ 19 and the ratio of the price of wheat per kg in shops A, B and C is 5 ∶ 8 ∶ 9 respectively. If the ratio of price of (3 kg rice + 2 kg wheat from shop A), (5 kg rice and 7 kg of wheat from shop B) and (5 kg rice from shop C and Rs. 135 worth other materials from shop B) is 2 ∶ 7 ∶ 6. What is the price of 25 kg of rice from shop A and 15 kg of wheat of shop B? (in rupees) Correct Answer 1350

Let the prices of rice per kg from shop A, B and C be 10a, 14a and 19a respectively

Let the prices of wheat per kg from shops A, B and C be 5b, 8b and 9b respectively

Price of 3 kg rice and 2 kg wheat from shop A = 30a + 10b

Price of 5 kg rice and 7 kg wheat from shop B = 70a + 56b

Price of 5 kg rice from shop C and Rs. 135 worth other materials from shop C = 95a + 135

Ratio given = 2 ∶ 7 ∶ 6

⇒ (30a + 10b)/(70a + 56b) = 2/7

⇒ 210a + 70b = 140a + 112b

⇒ 70a = 42b

⇒ a = 0.6b

⇒ (70a + 56b)/(95a + 135) = 7/6

⇒ (70 × 0.6b + 56b)/(95 × 0.6b + 135) = 7/6

⇒ 98b/(57b + 135) = 7/6

⇒ 588b = 399b + 945

⇒ 189b = 945

∴ b = 5

⇒ a = 0.6 × 5 = 3

⇒ Price of 25 kg rice from shop A and 15 kg wheat from shop B = 25 × 10a + 15 × 8b

⇒ 750 + 600 = Rs. 1350

∴ Required answer is Rs. 1350.

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