30% of Paul's savings was $66 more than 40% of Vaidev's savings. After Paul spent ¹₄ of his savings and Vaidev spent 40% of his savings, Paul had $195 more than Vaidev. How much was Paul's saving at first?

	Vaidev	Paul
Before	15 u	20 u + 220
Change	- 6 u	- 5 u - 55
After	9 u	15 u + 165
Comparing Vaidev and Paul in the end		195 more

30% = ³⁰₁₀₀ = ³₁₀

40% = ⁴⁰₁₀₀ = ²₅

³₁₀ Paul = ²₅ Vaidev + 66 

Make the numerators the same. LCM of 3 and 2 is 6.
 
3x210x2 Paul = 2x35x3 Vaidev + 66 
620 Paul = 615 Vaidev + 66 

Simplify the fractions.
¹₂₀ Paul = ¹₁₅ Vaidev + 11

Let ¹₁₅ Vaidev be 1 u.

Vaidev's savings at first = 15 u

¹₂₀ Paul = ¹₁₅ Vaidev + 11
Let ¹₂₀ Paul be 1 u + 11.

Paul's savings at first
= 20 x (1 u + 11) 
= 20 u + 220

Savings that Vaidev spent
= 40% x 15 u
= ⁴⁰₁₀₀ x 15 u
= 6 u

Savings that Paul spent 
= ¹₄ x (20 u + 220)
= 5 u + 55 

Paul had $195 more than Vaidev in the end. If another $195 was given to Vaidev, the amount that each had in the end would be the same.

15 u + 165 = 9 u + 195 
15 u - 9 u = 195 - 165
6 u = 30

1 u = 30 ÷ 6 = 5

Savings that Paul had at first
= 20 u + 220
= 20 x 5 + 220
= 100 + 220
= $320

Answer(s): $320