Question

Two numbers are in the ratio 7 :11. If 7 is added to each of the numbers, the ratio becomes 2:3. Find the

numbers.
​

Answer 1

Answer:

Let x and y are two numbers

According to the question

y

x

=

11

7

x=

11

7y

.......(i)

Now,

y+7

x+7

=32

3x+21=2y+14

3x=2y−7......(ii)

Substitute value of x from (i) to (ii)

3(

11

7y

)=2y−7

21y=22y−77

y=77

x=

11

7y

x=

11

7×77

x=7×7

x=49

Therefore the numbers are 49 and 77

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Answer 2

Answer:

x= 98 and y = 154

Solution:

let the no.s be x and y respectively.

Given:

x:y = 7:11

or 11x = 7y ……………eq1

or, x = 7y/11

and x+7 : y+7 = 2:3

or 3(x+7) = 2(y+7) ………………eq2

Putting value of x from equation 1 in eq2 :

3((7y/11)+7) = 2(y+7)

or 3(7y + 77)/11 = 2(y+7)

or 21y + 231 = 22y + 77

or 231 - 77 = 22y - 21y

or 154 = y

Putting value of y in eq1 :

x : 154 = 7 : 11

x = 154*7 : 11 = 14*7 = 98

x= 98 and y = 154

hope it helps.