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Q.

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 32. Find the rational number. 

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a

512

b

1921

c

1321

d

711

answer is B.

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Detailed Solution

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Let the numerator be x then the denominator = x+8 

∴ The rational number formed = xx+8 

According to the question, by adding 17 to numerator and subtracting 1 from denominator we get, 

 x+17(x+8)1=32        (It is given that the new rational number is equal to 32

 x+17(x+7)=32 

2(x+17)=3(x+7)    (by cross multiplying the equation) 

2x+34=3x+21 

2x3x=2134 

x=13 

x=13 

And, x+8=13+8=21 

Therefore, numerator = 13 and denominator = 21 

Hence, the required rational number is 1321.

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