Question

If a and b are integers of opposite signs such that (a + 3)² : b²  =  9 : 1 and (a - 1)² : (b - 1)² = 4 : 1, then the ratio a² : b² is?
1. 9 : 4
2. 81 : 4
3. 1 : 4
4. 25 : 4

Answer 1

Correct Answer - Option 4 : 25 : 4

Calculation:

⇒ Let we consider given ratios

⇒ (a + 3)² : b² = 9 : 1

⇒ (a + 3)/b = ± 3 

⇒ a + 3 = +3b ..... (1)

⇒ a + 3 = - 3b ..... (2)

⇒ Similarly we can solve for second ratio

⇒ (a - 1)/(b - 1) = ± 2 .... (3)

⇒ By solving equation (1) and (3)

⇒ a = 3, 3/5 and, b = 2, 6/5 So this is not possible because a and b are in opposite sign

⇒ Similarly by solving equation (2) and (3)

⇒ a = -9/5, 15 and b = -2/5, and -6

⇒ Where a = 15 and b = - 6 are possible

⇒ Now a² : b² = 25 : 4

∴ The required result will be 25/4.