Question

. The ratio of the ages of veer and Vikram 15 years ago was 2 :1 and their ages difference 5 years ago was 10 years, then find out the ratio of ages of Veer and Vikram 15 years hence?​

Answer 1

Step-by-step explanation:

Let the present age of Veer be 'x' years and the present age of Vikram be 'y' years. Given that their ages difference 5 years ago was 10 years. So, age difference between them will be same. Ratio of their ages after 15 yrs = 50 : 40 = 5 : 4.

Answer 2

$\frac { \text{Age of veer after 15 years}}{ \text{Age of vikram after 15 years}} = \bf \red{ \frac{5}{4}}$

Given:

• The ratio of the ages of veer and Vikram 15 years ago was 2 :1 and,
• Their ages difference 5 years ago was 10 years.

To find:

• Find out the ratio of ages of Veer and Vikram 15 years hence?

Solution:

Step 1:

Let the present age of veer is 'x' years and that of Vikram's is 'y' years.

Ages of veer and vikram before 15 years are (x-15) years and (y-15) years respectively.

ATQ

$\frac{x - 15}{y - 15} = \frac{2}{1}$

cross multiply

$x - 15 = 2y - 30$

or

$\bf x - 2y = - 15...eq1$

Step 2:

Ages of veer and vikram before 5 years are (x-5) years and (y-5) years respectively.

ATQ

$x - 5 - (y - 5) = 10$

or

$\bf x - y = 10...eq2$

Step 3:

Solve eq1 and eq2.

Subtract both equations.

$x - 2y = - 15 \\ x - y = 10 \\ ( - ) \: \: ( + ) \: \: ( - ) \\ - - - - - - - \\ - y = - 25 \\ - - - - - - -$

or

$\bf y = 25$

put the value of y in eq2.

$x - 25 = 10$

or

$\bf x = 35$

Present ages of veer and vikram are 35 years and 25 years respectively.

Step 4:

Find the ages of both after 15 years.

Age of veer after 15 years is: 35+15= 50 years

Age of vikram after 15 years is: 25+15= 40 years

Step 5:

Find the ratio of ages of both after 15 years.

$\frac { \text{Age of veer after 15 years}}{ \text{Age of vikram after 15 years}} = \frac{50}{40}$

or

Thus,

Ratio is $\frac { \text{Age of veer after 15 years}}{ \text{Age of vikram after 15 years}} = \frac{5}{4}$

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