Question

Two numbers are in the ratio 4:5 if 6 is added to the first number and 8 to the other number the ratio becomes 11:14 find the numbers

Answer 1

let the two numbers are 4x and 5x
then
after adding 6 to the first number and 8 to the second number the ratio = 11:14

4x+6/(5x+8) = 11:14

14(4x+6)=11(5x+8)

56x+84=55x+88

56x-55x =88-84

x=4

there fore required numers are

first = 4x = 4×4 =16

second = 5x =5×4=20

Answer 2

✬ Numbers are 16 & 20 ✬

Step-by-step explanation:

Given:

• Two numbers are in ratio 4 : 5.
• After adding 6 to first number and 8 to second number the ratio becomes 11 : 14.

To Find:

• What are these two numbers ?

Solution: Let x be the common in given ratios. Therefore numbers become 4x and 5x.

Here,

• First number = 4x
• Second number = 5x

[ Adding 6 to first number ]

➙ First Number = 4x + 6

[ Adding 8 to second number ]

➙ Second Number = 5x + 8

A/q

• After adding 6 & 8 to both number the ratio becomes 11 : 14

$\implies{\rm }$ (4x + 6) : (5x + 8) = 11 : 14

$\implies{\rm }$ (4x + 6)/(5x + 8) = 11/14

$\implies{\rm }$ 14 (4x + 6) = 11 (5x + 8)

$\implies{\rm }$ 56x + 84 = 55x + 88

$\implies{\rm }$ 56x – 55x = 88 – 84

$\implies{\rm }$ x = 4

So,

➟ First Number = 4x = 4 $\times$ 4 = 16

➟ Second Number = 5x = 5 $\times$ 4 = 20