UPSC CDS 2 2021 Math Paper

Given,
Sum of numerator and denominator of fraction is 10 .
Let the numerator be x.
Then, denominator =10−x
According to the question,
‌

x+3

(10−x)−1

=1
⇒‌‌‌

x+3

9−x

=1
⇒‌‌x+3=9−x
⇒‌‌2x=6
⇒‌‌x=3
∴‌‌‌ Numerator ‌=3‌ and denominator ‌
‌‌‌=10−3=7
∴‌‌ Difference ‌
‌‌=‌ Denominator ‌−‌ Numerator ‌
‌‌=7−3=4
Hence, the required difference is 4 .