Question

two number are in the ratio of 4;5 ,if we subtract 6 from each number the ratio will become 3:4.find the sum of both the number​

Answer 1

Solution

Given That :-

• Ratio of two number = 4 : 5
• if we subtract 6 from each number the ratio will become 3:4.

Find :-

• Sum of both the Number

Explanation

Let,

• First Number be = x
• Second Number be = y

Case(1).

(Ratio of two number = 4 : 5)

A/C to question,

==> x : y = 4 :5

==> x/y = 4/5

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

Case(2).

(if we subtract 6 from each number the ratio will become 3:4)

==> (x-6) : (y-6) = 3:4

==> (x-6)/(y-6) = 3/4

==> 4*(x-6) = 3*(y-6)

==> 4x - 3y = -18 + 24

==> 4x - 3y = 6 ----------------(2)

Multiply by 4 in equ(1) & 5 in equ(2)

• 20x - 16y = 0
• 20x - 15y = 30

__________________Sub. it's

==>-16y + 15y = -30

==> -y = -30

==> y = 30

Keep Value of y in equ(1)

==> 5x - 4*30 = 0

==> 5x = 120

==> x = 120/5

==> x = 24

Hence

• First Number will be (x) = 24
• Second Number will be (y) = 30

_________________

Answer 2

$\bf\huge {ANSWER}$

Let the numbers be 4x and 5x .

According to the question ,

$\rm\longrightarrow \dfrac{4x-6}{5x-6} =\dfrac{3}{4}\\\\\longrightarrow 4(4x-6)=3(5x-6)\\\\\longrightarrow 16x-24=15x-18\\\\\longrightarrow 16x-15x=24-18\\\\\longrightarrow\bf \underline{ x=6}$

The two numbers are 24 and 30 .

HOPE IT HELPS U ..............