## Two numbers are in the ratio 9.4. If 7 is added to each of the numbers, the ratio becomes 5:3. Find the numbers.​

Question

Two numbers are in the ratio 9.4. If 7
is added to each of the numbers, the
ratio becomes 5:3. Find the numbers.​

in progress 0
4 weeks 2021-08-17T15:17:51+00:00 2 Answers 0 views 0

## Answers ( )

1. Answer:

18 and. 8

Step-by-step explanation:

As the ratio is 9:4, let the numbers are 9a and 4a.

According to question: when 7 is added to both new numbers are 9a + 7 and 4a + 7.

= > ( 9a + 7 ) : ( 4a + 7 ) = 5:3

= > 3( 9a + 7 ) = 5( 4a + 7 )

= > 27a + 21 = 20a + 35

= > 27a – 20a = 35 – 21

= > 7a = 14

= > a = 14/7 = 2

Hence the numbers are :

9a = 9(2) = 18

4a = 4(2) = 8

2. ### EXPLANATION.

• GIVEN

Two number are in the ratio = 9:4

If 7 is added to each of the number, the ratio

becomes = 5:3

### According to the question,

Let one number be = x

Let another number be = y

### Case = 1

Two numbers are in the ratio = 9:4

=> x/y = 9/4

=> 4x = 9y

=> 4x – 9y = 0 ……(1)

### Case = 2

if 7 is added to the number the ratio = 5:3

=> x + 7 / y + 7 = 5/3

=> 3 ( x + 7 ) = 5 ( y + 7 )

=> 3x + 21 = 5y + 35

=> 3x – 5y = 14 …… (2)

From equation (1) and (2) we get,

multiply equation (1) by 3

multiply equation (2) by 4

we get,

=> 12x – 27y = 0

=> 12x – 20y = 14

we get,

=> – 7y = -14

=> y = 2

put the value of y = 2 in equation (2)

we get,

=> 3x – 5y = 14

=> 3x – 5(2) = 14

=> 3x – 10 = 14

=> 3x = 24

=> x = 8