Question

10 years ago, the ratio of Marcy's age to Brenda's age was 2 : 5. The difference in their ages was 9 years. what is the ratio of Mercy's age to Brenda's age now?

Answer 1

Answer:

10 years ago, let mercy's age be 2x & Brenda's age be 5x

then, 5x-2x =9

or, 3x = 9

or, x= 3

so , Mercy was 6 & Brenda was 15 .

now , Mercy is 16 & Brenda is 25

Answer 2

Answer:

• Ratio of present ages of Mercy and Brenda is 16 : 25

Explanation:

Let, present ages of Mercy and Brenda be x and y respectively

then,

10 yrs ago the ratio of Mercy's age to Brenda's age was 2 : 5

therefore,

→ ( x - 10 ) / ( y - 10 ) = 2 / 5

cross multiplying

→ 5 x - 50 = 2 y - 20

→ 5 x - 2 y - 50 + 20 = 0

→ 5 x - 2 y - 30 = 0   ____equation (1)

and, difference in their ages was 9 years so,

→ ( y - 10 ) - ( x - 10 ) = 9

→ y - 10 - x + 10 = 9

→ y - x = 9

→ x = y - 9   ___equation (2)

substituting value of equation (2) in equation (1)

→ 5 x - 2 y - 30 = 0

→ 5 ( y - 9 ) - 2 y - 30 = 0

→ 5 y  - 45 - 2 y - 30 = 0

→ 3 y - 75 = 0

→ 3 y = 75

→ y = 25  

putting value of y in equation (2)

→ x = y - 9

→ x = ( 25 ) - 9

→ x = 16

Therefore,

Present ages of Mercy and Brenda are 16 years and 25 years respectively.

so,

→ Ratio of their present ages = 16 / 25

Hence,

• Ratio of present ages of Mercy and Brenda is 16 : 25.