Two numbers are such that the ratio between them is 3:5. if each is increased by 10, the ratio between the new numbers so formed is 5:7.find the original numbers.
Answers
Answer:
Original numbers are 15 and 25.
Step-by-step explanation:
Let x and y be the two numbers .
Now,
CASE 1 :
→ Two numbers are such that the ratio between them is 3 : 5.
ATQ,
∵ x : y = 3 : 5
⇒ 5x = 3y
∵ x = 3y / 5 ........( 1 )
CASE 2 :
→ If each number in increased by 10, the ratio between the new number so formed is 5 : 7.
ATQ,
∵ ( x + 10 ) : ( y + 10 ) = 5 : 7
⇒ 7( x + 10 ) = 5( y + 10 )
⇒ 7x + 70 = 5y + 50
⇒ 7x + 70 - 50 = 5y
⇒ 7x + 20 = 5y ........( 2 )
Put value of 'x' from eqⁿ ( 1 ) in ( 2 ) .
⇒ 7× 3y / 5 + 20 = 5y
⇒ ( 21y + 100 ) / 5 = 5y
⇒ 21y + 100 = 25y
⇒ 100 = 25y - 21y
⇒ 100 = 4y
⇒ 100 / 4 = y
∴ y = 25
Therefore,
∵ y = 25
Put y = 25 in eqⁿ ( 1 ), we get
⇒ x = 3 × 25 / 5
⇒ x = 3 × 5
∴ x = 15
Original numbers are x and y = 15 and 25.
Thanks ..!!!
Answer:
original numbers are 15 and 25
Step-by-step explanation:
3x + 5x are the two numbers
if 10 is added
3x+10+5x+10=5x+7x
8x+20=12x
20=12x-8x
20= 4x
x= 20/4
x= 5
then 3x = 3*5= 15
5x = 5*5= 25
HOPE THIS HELPS YOU