Question

The present age of Roy and his mother are in the ratio 2:5. After 4 years, the ratio of their
ages becomes 5:11 respectively. What are their present ages?

Answer 1

Answer:

Roy is 16 and mother is 40

Answer 2

Solution :-

Let us assume that, present age of roy and his mother is 2x and 5x years .

so,

→ After 4 years roy age = (2x + 4)

and,

→ Roy's mother age will be = (5x + 4)

A/q,

→ (2x + 4)/(5x + 4) = 5/11

→ 11(2x + 4) = 5(5x + 4)

→ 22x + 44 = 25x + 20

→ 25x - 22x = 44 - 20

→ 3x = 24

→ x = 8

therefore,

→ Present age of roy = 2x = 2 * 8= 16 years .

→ Present age of roy's mother = 5x = 5 * 8 = 40 years

Ratio Method :-

→ Roy(Present) : Mother(Present) = 2 : 5

→ Roy(4 years later) : Mother (4 years later) = 5 : 11

so,

→ Roy(Present) : Mother(Present) = 6(2 : 5) = 12 : 30

→ Roy(4 years later) : Mother (4 years later) = 3(5 : 11) = 15 : 33

then,

→ 15 - 12 = 33 - 30 = 3 unit .

therefore,

→ 3 unit = 4

→ 1 unit = (4/3)

hence,

→ Roy present age = 12 unit = 12 * (4/3) = 16 years .

→ Roy's mother present age = 30 unit = 30 * (4/3) = 40 years.

Hence, Roy present age is 16 years and his mother present age is 40 years .

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