Question

ת וטווחfro
The ages of Radha and Sudha are in the ratio 4:5. Two years from
be in the ratio 5:6. Find their present ages.
​

Answer 1

Answer:

Present age of Radha = 8 years

Present age of Sudha = 10 years

Step-by-step explanation:

Given--->

-----------

The present ages of Radha and Sudha are in the ratio 4:5 and two years from now ages be in the ratio 5:6

To find --->

------------

Present ages of Radha and Sudha

Solution--->

---------------

Let present ages of Radha and Sudha be x and y years

ATQ x : y = 4 : 5

=> x / y = 4 / 5

=> x =( 4 / 5) y

After two years age of Radha = x + 2

After two years age of Sudha = y + 2

ATQ (x + 2 ) : ( y + 2 ) = 5 : 6

=> ( x + 2 ) / ( y + 2 ) = 5 / 6

=> 6 ( x + 2 ) = 5 ( y + 2 )

=> 6 x + 12 = 5 y + 10

=> 6x - 5 y = 10 - 12

=> 6x - 5 y = -2

Putting x = 4/5 y in it

=> 6 (4/5 y ) - 5 y = -2

24 y -25 y

=> -------------------- = -2

5

- y

=> --------- = -2

5

=> - y = - 10

=> y = 10

x =( 4/5) y

Putting y = 10 in it

x = (4 / 5 ) 10

= 4 × 2

= 8

Present age of Radha = x

= 8 years

Present age of Sudha = y

= 10 years

Answer 2

SOLUTION:-

Given:

The ages of Radha & Sudha are in the ratio 4:5.Two years from be in the ratio 5:6.

To find:

The present age of Radha and Sudha.

Explanation:

Let the present age of Radha be R years.

Let the  present age of Sudha be M years.

Therefore,

R:M=4:5

$\frac{R}{M} =\frac{4}{5}$

[Cross Multiplication]$\frac{R+2}{M+2} =\frac{5}{6}$

$5R=4M\\\\R=\frac{4M}{5} .............(1)$

∴According to the question:

• After two years the age of Radha & Sudha :

• Age of Radha after two years= (R+2) years.
• Age of Sudha after two years=(M+2) years.

Then the ratio formed 5:6.

(R+2):(M+2)=5:6

$\frac{R+2}{M+2} =\frac{5}{6}$

[Cross Multiplication]

→6(R+2)=5(M+2)

→6R+12=5M+10

→6R-5M=10-12

→6R-5M= -2

Using the place of R from equation (1), we get;

$6(\frac{4M}{5} )-5M=-2\\\\\frac{24M}{5} -5M=-2\\\\24M-25M=-10\\\\-M=-10\\\\M=10 years$

Using the value of M in equation (1), we get;

R= 4(10)/5

R= 40/5

R= 8 years

Thus,

• The present age of Radha is 8 years.
• The present age of Sudha is 10 years.