Question : A, B, and C received an amount of Rs. 8400 and distributed it among themselves in the ratio 6 : 8 : 7, respectively. If they save in the ratio of 3 : 2 : 4, respectively, and B saves Rs. 400, then what is the ratio of the expenditures of A, B, and C respectively?
Option 1: 6 : 8 : 7
Option 2: 8 : 6 : 7
Option 3: 9 : 14 : 10
Option 4: 12 : 7 : 9
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Correct Answer: 9 : 14 : 10
Solution :
Given: A, B, and C received an amount of Rs. 8400.
The sum A will receive $= 6 ×\frac{8400}{6+8+7} = 6 × \frac{8400}{21} = 2400$
Amount B will receive $= 8 × \frac{8400}{6+8+7} = 8 × \frac{8400}{21}= 3200$
The amount C will receive $= 7 × \frac{8400}{6+8+7} = 7 × \frac{8400}{21} = 2800$
Assume that A, B, and C have saved $3y, 2y,$ and $4y$ respectively.
Also, it is given that B saves money which is $2y = 400 ⇒ y = 200$
The amount saved by A, B, and C is 3 × 200 = Rs. 600, 2 × 200 = Rs. 400, and 4 × 200 = Rs. 800 respectively.
Their expenditure can be expressed as follows,
Expenditure of A = 2400 – 600 = Rs. 1800
Expenditure of B = 3200 – 400 = Rs. 2800
Expenditure of C = 2800 – 800 = Rs. 2000
The ratio of their expenditure = 1800 : 2800 : 2000 = 9 : 14 : 10
So, the ratio of expenditure of A : B : C = 9 : 14 : 10
Hence, the correct answer is 9 : 14 : 10.
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