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Question

Two natural numbers are such that their product, sum and difference are in the ratio 24 : 7 : 1. The product of the two numbers is __________.

A
48
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B
24
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C
12
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D
6
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Solution

The correct option is A 48
Let the numbers be x and y.
xy:(x+y):(xy)=24:7:1∴xy:(x+y):(x−y)=24:7:1
x+yxy=71∴x+yx−y=71
or, 7x7y=x+y6x=8y7x−7y=x+y⟹6x=8y
or, x=4y3x=4y3
Again, xyx+y=247xyx+y=247
or, 43y243y+y=2474y7=24743y243y+y=247⟹4y7=247
y=6∴y=6 and x=8x=8
Product of the both numbers =8×6=48=8×6=48.

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