Question

Three years ago, the ratio of ages of A and B was 7:1. After three years from 110w, the ratio of their ages will be 4:1. What is the difference between their ages (in years) after seven years from now?​

Answer 1

Question :

Three years ago, the ratio of ages of A and B was 7:1. After three years the ratio of their ages will be 4:1. What is the difference between their ages (in years) after seven years from now?

To find :

The difference of their ages after 7 years

Solution :

Let us assume

A's age be 7x

B's age be x

So, Their present ages are

A → 7x + 3

B → x + 3

Here we added three because it is telling 3 years after

Age of A, 3 yrs from now = 7x + 3 + 3 = 7x + 6 yrs

Age of B, 3 yrs fr now = x + 3 + 3 = x + 6 yrs

The ratio is given 4 : 1

Then,

$\sf \small \rarr\frac{7x + 6}{x + 6} = \frac{4}{1}$

By cross multiplication we get

$\sf \small \rarr1(7x + 6) = 4(x + 6)$

By simplifying we get

$\sf \small \rarr7x + 6 = 4x + 24$

Taking the variables on the L.H.S. and the numbers on the R.H.S. we get

$\sf \small \rarr7x - 4x = 24 - 6$

$\sf \small \rarr3x = 18$

$\sf \small \rarr x = \frac{18}{3} = 6$

So the value of x is 6

Now putting 6 instead of x we get

7x + 3

→ 7 × 6 + 3

→ 42 + 3

→ 45

x + 3

→ 6 + 3

→ 9

Now,

Age of A after 7 yrs = 45 + 7 → 52 yrs

Age of B after 7 yrs = 7 + 9 → 16

Difference = 52 – 16

= 36

So the difference in their ages after 7 yrs is 36

Answer 2

Question :

• Three years ago, the ratio of ages of A and B was 7:1. After three years the ratio of their ages will be 4:1. What is the difference between their ages (in years) after seven years from now?

To find :

• The difference of their ages after 7 years

Solution :

Let us assume

• A's age be 7x

• B's age be x

• So, Their present ages are

• A → 7x + 3

• B → x + 3

• Here we added three because it is telling 3 years after

• Age of A, 3 yrs from now = 7x + 3 + 3 = 7x + 6 yrs

• Age of B, 3 yrs from now = x + 3 + 3 = x + 6 yrs

• The ratio is given 4 : 1

Then,

• 7x+6/x+6 = 4/1

By cross multiplication we get

• →1(7x+6)=4(x+6)

By simplifying we get

• →7x+6=4x+24

• Taking the variables on the L.H.S. and the numbers on the R.H.S. we get

• →7x−4x=24−6

• 3x=18

• x = 18/3 = 6

• So the value of x is 6

• Now putting 6 instead of x we get

• 7x + 3

• → 7 × 6 + 3

• → 42 + 3

• → 45

• x + 3

• → 6 + 3

• → 9

Now,

• Age of A after 7 yrs = 45 + 7 → 52 yrs

• Age of B after 7 yrs = 7 + 9 → 16

• Difference = 52 – 16

• = 36

• So the difference in their ages after 7 yrs is 36