❏ Question

Two number are such that the ratio between them is 3: 5 if each is increased by 10 the ratio between the new number so formed is 5:7 find the original number

❏ Solution

GIVEN:-

• Ratio of between two number is 3:5
• If each number increase by 10 the ratio will be 5:7

FIND:-

• Original two number

❏ EXPLANATION

Let,

• First number = x
• Second number = y

A/c to question,

( Ratio of between two number is 3:5 )

➥ x : y = 3 : 5

➥ x/y = 3/5

➥ 5x - 3y = 0 ..................Equ(1)

Again,

( If each number increase by 10 the ratio will be 5:7 )

➥ (x + 10) : (y + 10) = 5 : 7

➥ (x + 10) / (y + 10) = 5 / 7

➥ 7(x+10) = 5(y+10)

➥ 7x - 5y = 50 - 70

➥ 7x - 5y = -20 ..............Equ(2)

Multiply by 7 in equ (1) and 5 in equ(2),

• 35x - 21y = 0
• 35x - 25y = - 100

_______________Sub. it's

➥ ( -21y + 25y) = 100

➥ 4y = 100

➥ y = 100/4

➥ y = 25

Keep VALUE of y in equ(1),

➥ 5x - 3 × 25 = 0

➥ 5x = 75

➥ x = 75/5

➥ x = 15

THUS:-

• First number will be = 15
• Second number will be = 25

❏ Verification

CASE(1):-

( Ratio of between two number is 3:5 )

➥ X:Y = 3:5

write in division form

➥ x/y = 3/5

keep value of x and y

➥ 15/25 = 3/5

Divide by 5

➥ 3/5 = 3/5

➥ 3:5 = 3:5

L.H.S = R.H.S

CASE(2):-

( If each number increase by 10 the ratio will be 5:7 )

➥ (X+10):(Y+10) = 5:7

write in division form

➥(X+10)/(Y+10)=5/7

keep value of x and h

➥ (15+10)/(25+10) =5/7

➥ 25/35 = 5/7

Divide by 5

➥ 5/7 = 5/7

➥ 5:7 = 5:7

L.H.S = R.H.S

both cases are satisfied .

So, our solution is right !!