Question

The age of A is five years more than that of B. 5 years ago the ratio of their ages was 3:2. Find their present ages

Answer 1

Age of B = X

Age of A= X+5

5 years ag , the ratio was 2:3 ( I reversed the ratio cuz I took B first)

2/3 = X/X+5

Now by cross multiplying

2(X+5)=3X

=> 2X + 10 = 3X

=> X = 10

Which means before 5 years , the age of B was 10 and the age of A was 15 and now , which is 5 years later the age of B is 15 and age of A is 20

let age of A be x years.

let age of B be y years.

from given information:

x=y+5

and, (x-5)/(y-5)=3/2

thus,(y+5–5)/(y-5)=3/2 {since x=y+5}

y/(y-5)=3/2

2y=3(y-5) {by cross multiplication}

thus, 2y=3y-15

2y-3y=-15

-y=-15

y=15

since y=15,x=15+5=20

so,y=15,x=20

Clearly,present ages of A and B are 20 and 15 years respectively.

It has an easy solution.

Ratio is given 3:2.

Difference of age is 5 years.

So 1 unit is equal to 5.

So age of A = 3*5=15

Age of B = 2*5 = 10…

Present age of A is 15+5= 20

Similarly present age of B is 10+5 = 15.

Answer 2

Answer:

Let age of B = x

Let age of A = x + 5

5 years ago, the ratio was 3:2

According to the question

(by cross multiplication)

3x = 2x + 10

3x-2x = 10

x = 10

Age of B = 10 years

Age of A = 10 + 5 = 15 years

5 years later,

Age of B = x + 5 = 10 + 5 = 15 years

Age of A = x + 5 + 5 = 10 + 10 = 20 years