SOLUTION: Jaya is 10 yrs younger than Sid. If you increase both of their ages by 20 %, the difference between their ages is 18 less than Jayas current age. How old is Sid?

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Question 522650: Jaya is 10 yrs younger than Sid. If you increase both of their ages by 20 %, the difference between their ages is 18 less than Jayas current age. How old is Sid?
Answer by Maths68(1474) About Me  (Show Source):
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Let
Current age of Jaya = j
Current age of Sid = s
Jaya is 10 yrs younger than Sid
s=j+10..............(1)
increase both of their ages by 20 %
Sid = s * 20/100 = s/5
Jaya = j * 20/100 = j/5
Then
Jaya will be = j + j/5 = (5j + j)/5 = 6j/5
Sid will be = s + s/5 = (5s+s)/5 = 6s/5
The difference between their ages is 18 less than Jayas current age.
The difference between their ages is 18 less than Jayas current age.
6s/5-6j/5 = 18-j
Multiply by 5 both sides of the equation
6s-6j=90-5j
6s-6j+5j=90
6s-j=90................(2)
Put the value of s from (1) to (2)
6(j-10)-11j=90
6j-60-j=90
5j=90+60
5j=150
5j/5=150/5
j=30
Put the value of j in (1)
s=j+10
s=30+10
s=40

Current age of Jaya = j = 30
Current age of Sid = s = 40

Check
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If you increase both of their ages by 20 %, the difference between their ages is 18 less than Jayas current age
(40+40(20/100)) - (30+30(20/100)) = 30-18
(40+40(1/5))-(30+30(1/5))=12
(40+8)-(30+6)=12
48-36=12
12=12