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
Answers
❏ 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 !!
Step-by-step explanation:
Two number are in the ratio = 3: 5
then first number is = 3x
second number is = 5x
each is increased by 10
then, the ratio will be 3x+10/5x+10
the ratio between the new numbers so formed is 5:7
3x+10/5x+10 = 5/7
cross multiplication
21x+70 = 25x+50
4x = 20
x = 5
then, the first number is 15 and the second number is 25
Hope this helps you