1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, the number becomes 32. The original number is:

A

8/11

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

5/8

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

7/10

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

2/5

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A 8/11 Let numerator of the rational number be x. Then denominator of the rational number can be written as (x+3) Thus the rational number is xx+3 When the numerator is increased by 7, it becomes (x+7) When the denominator is decreased by 1, it becomes (x+3−1) The new number formed = 32 So, (x+7)(x+2)=32 By cross multiplication, ⇒2(x+7)=3(x+2) ⇒ 2x+14=3x+6 ⇒ (3x−2x)=(14−6) [Grouping like terms] ⇒x=8 ⇒The numerator of the rational number =x=8 ⇒ The denominator of the rational number = (x+3)=8+3=11 Hence, the original number is 811

Suggest Corrections
8
Join BYJU'S Learning Program
Related Videos
MATHEMATICS
Watch in App
Join BYJU'S Learning Program