Question

two numbers are in the ratio 4:5. If 5 is added to each number, tgeir ratio become 13:16. Find the numbers.​

Answer 1

EXPLANATION.

Let the one number be = x

Let the another number be = y

Case = 1.

Two number are in ratio = 4:5

=> x/y = 4/5

=> 5x = 4y

=> 5x - 4y = 0 ......(1)

Case = 2.

If 5 is added to the number their ratio

become = 13:16

=> x + 5 / y + 5 = 13/16

=> 16 ( x + 5 ) = 13 ( y + 5 )

=> 16x + 80 = 13y = 65

=> 16x - 13y = -15 ......(2)

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

=> multiply equation (1) by 13

=> multiply equation (2) by 4

we get,

=> 65x - 52y = 0

=> 64x - 52y = -60

we get,

=> x = 60

put the value of x = 60 in equation (1)

we get,

=> 5(60) - 4y = 0

=> 300 - 4y = 0

=> y = 300/4

=> y = 75

Therefore,

The number are = 60 and 75

Answer 2

Answer:

The numbers are 60 and 75.

Step-by-step explanation:

Given, that the two numbers are in the ratio 4:5.

Let the first number be 4x while the second number be 5x.

If 5 is added to each number then

The first number is 4x + 5 while the second number is 5x +5.

Now it is given that

4x + 5 : 5x+5 = 13:16

This implies,

$\frac{4x + 5}{5x + 5} = \frac{13}{16}\\ (4x+5)*16 = (5x+5)*13\\64x+80 = 65x+65\\80 - 65 =65 x -64 x\\15 = x$

Thus, x = 15.

The first number is in the form of 4x while the other number is of the form 5x.

Substituting the value of x ,we get

First number = 4 * 15

                     = 60

Second number = 5 * 15

                           = 75.

"Therefore the numbers are 60 and 75."

Thank you