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
• B. 24
• C. 12
• D. 6

Answer 1

The correct option is A 48

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