Question

# If (B - A) of 30% = (B + A) of 18% , So Ratio A : B equals to? (A) 4:1 (B) 1:4 (C) 5:4 (D) 5:9

Solution

I = ∫^∞_0 dx/(x+√x^2+1)^3

Put x = taut ⇒dx = sec² + dt

⇒ I = π/2∫_0 sec²+dt/(taut+√ 1+tan²t)^3

Given :- (B-A)×30% = (B+A)×18%

∴ (B-A) 30/100 = (B+A) ×18/100

(B-A) 10 = (B+A)×6

(B-A)5 = (B+A)3

5B-5A = 3B+3A

2B = 8A

∴ 2/8 = A/B

⇒ A/B = 1/4

**Thus, A:B = 1:4.**