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Question

Mr. and Mrs. Ahuja weigh x kg and y kg respectively. They both take a dieting course, at the end of which Mr. Ahuja loses 5 kg and weighs as much as his wife weighed before the course. Mrs. Ahuja loses 4 kg and weighs 78 th of what her husband weighed before the course. Form two equations in x and y, find their weights before taking the dieting course.

A
Mr. Ahuja= 32 kg and Mrs. Ahuja= 45 kg
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B
Mr. Ahuja= 72 kg and Mrs. Ahuja= 67 kg
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C
Mr. Ahuja= 78 kg and Mrs. Ahuja= 51 kg
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D
Mr. Ahuja= 39 kg and Mrs. Ahuja= 63 kg
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Solution

The correct option is B Mr. Ahuja= 72 kg and Mrs. Ahuja= 67 kg
Given, at the end of dieting course, Mr. Ahuja loses 5 kg and weighs as much as his wife weighed before the course
=>x5=y
=>xy=5 ...(1)
Mrs. Ahuja loses 4 kg and weighs 78th of what her husband weighed before the course.
y4=78x
7x8y=32 ....(2)

Multiplying equation (1) with 8 we get,

8x8y=40 ...(3)

Subtracting equation (2)from (3), we get

x=72

Substituting x=72 in the equation (1), we get

xy=5=>72y=5=>y=67

Hence, Mr Ahuja weighed 72kg and Mrs. Ahuja weighed 67 kg. before the dieting course.


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