Question

Two numbers are in ratio 2:1. If 4 is subtracted from both the numbers, ratio becomes 3:1. Find the
numbers.

Answer 1

Question

Two numbers are in ratio 2:1. If 4 is subtracted from both the numbers, ratio becomes 3:1. Find the numbers.

Solution

Given:-

• Ratio of two number = 2:1
• If subtract 4 from both number , ration became = 3:1

Find:-

• Two number

Explanation

Let,

• first number be x
• and second number be y .

A/c to question,

( Ratio of two number = 2:1 )

➠ x : y = 2:1

➠ x/y = 2/1

➠ x - 2y = 0 --------------(1)

Again

( If subtract 4 from both number , ration became = 3:1)

➠ (x-4):(y-4) = 3:1

➠(x-4)/(y-4) = 3/1

➠ (x-4) = 3.(y-4)

➠ x - 3y = -12 +4

➠ x - 3y = -8 ------------(2)

Subtract equation (1) to equation (2)

➠ (-2y + 3y ) = 0+8

➠ y = 8

keep value of y in equation (1),

➠ x - 2.(8) = 0

➠ x = 16

Thus

• Value of x = 16
• Value of y = 8

________________

Verification

Case(1):-

( Ratio of two number = 2:1 )

➠ x : y = 2:1

keep value of x and y

➠ (16) : (8) = 2:1

➠ 2:1 = 2:1

L.H.S. = R.H.S.

Again,

( If subtract 4 from both number , ration became = 3:1 )

➠ (x-4):(y-4) = 3:1

➠(16-4):(8-4) = 3:1

➠ 12 : 4 = 3:1

➠ 3:1 = 3:1

L.H.S. = R.H.S.

That's proved.