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A certain quantity of rice was divided into two parts in the ratio 2 ∶ 1 and placed in bags A and B respectively. Similarly, a certain quantity of wheat was divided into two parts in the ratio 2 ∶ 3 and placed in the bags C and D respectively. If the weight of bags A and D is equal, and the lightest bag weighs 12 kg, what is the total quantity of rice and wheat in the four bags?

A certain quantity of rice was divided into two parts in the ratio 2 ∶ 1 and placed in bags A and B respectively. Similarly, a certain quantity of wheat was divided into two parts in the ratio 2 ∶ 3 and placed in the bags C and D respectively. If the weight of bags A and D is equal, and the lightest bag weighs 12 kg, what is the total quantity of rice and wheat in the four bags? Correct Answer 76 kg

Let the quantity of rice in the bags A and B be ‘2x’ kg and ‘x’ kg respectively

Let the quantity of wheat in the bags C and D be ‘2y’ kg and ‘3y’ kg respectively

∵ Weight of bags A and D is equal,

⇒ 2x = 3y

⇒ x = (3/2)y

Hence,

Weight of bag A = 2x = 3y

Weight of bag B = x = (3/2)y = 1.5y

Weight of bag C = 2y

Weight of bag D = 3y

Thus, bag B is the lightest bag with a weight of 12 kg

⇒ x = 12

⇒ y = 12/1.5 = 8

∴ Total quantity of rice and wheat in 4 bags = 3y + 1.5y + 2y + 3y = 9.5y = 9.5(8) = 76 kg

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