UPSC CDS 2 2021 Math Paper

Let the age of father be x years and sum of the ages of his 4 children be y years.
⇒‌‌x=y . . . (i)
After 10 years, father's age =x+10 and sum of ages of 4 children =y+40
and sum of ages of 4 children =y+40
According to the question,
‌y+40=1.6(x+10)
⇒‌x+40=1.6(x+10)(‌ from Eq. (i)) ‌
⇒‌x+40=1.6x+16
⇒‌40−16=1.6x−x
⇒‌24=0.6x
⇒‌x=‌

24

0.6

=40
Hence, the present age of the father is 40yr.