Previous Year Questions

a² + a + 1 = 0 ... (i)

multiply a² + a + 1 = 0 by a

a³ + a² + a = 0 ... (ii)

Subtract (i) from (ii)

a³ - 1 = 0

a³ = 1

N = 2 * 1 = 2

Let the present age of D be 'X' year.

C's age four years hence = N² * X = 2² * X = 4X

C^'s present age = 4X - 4 years

A's age three years hence = (2N + 1) * X = (2*2 + 1) * X = 5X

A's present age = 5X - 3 years

A's present age - B's present age = 1/N * C's present age

5X - 3 - B's present age = 1/2 * (4X - 4)

5X - 3 - B's present age = 2X - 2

B's present age = 5X - 3 - 2X + 2 = 3X - 1 years

A/Q

5X - 3 - 7 + 3X - 1 + 1 + 4X - 4 - 1 + X + 5 = 30 * 4

13X - 10 = 120

13X = 130

X = 10

1)

A's age, three years hence - D's present age = 5X - 3 + 3 - X

= 5 * 10 - 10

= 40 years

2)

B's age, four years ago * 3 - C's present age = (3X - 1 - 4) * 3 - (4X - 4)

= (3 * 10 - 5) * 3 - (4 * 10 - 4)

= 25 * 3 - 36

= 39 years

3)

D's age, five years hence * 5 - A's present age = (X + 5) * 5 - (5X - 3)

= (10 + 5) * 5 - (5 * 10 - 3)

= 15 * 5 - 47

= 28 years

Hence, 1 - b, 2 - a, 3 - c.