two numbers are such that the ratio between them is 3:5 if it is increased by 5 then the ratio between the number so formed is 2:3 find the original number
Answers
Answer:
Step-by-step explanation:
let the two numbers are x and y
then,
x/y = 3/5
x=(3y) /5. ......(1)
also,
(x+10)/(y+10) = 5/7
7(x+10)=5(y+10)
7x = 5y+50-70=5y-20
put the value of x from eq. (1)
7(3y/5) =5y - 20
21y =25y - 100
25y-21y = 100
y = 100/4
y =25
put the value of y in eq.(1)
x = (3×25)/5
x=15
hence , the numbers are 15 and 25
or
Let x and y be the two numbers .
Now,
CASE 1 .
→ Two numbers are such that the ratio between them is 3 : 5.
A/Q,
∵ 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.
A/Q,
∵ ( x + 10 ) : ( y + 10 ) = 5 : 7 .
⇒ 7( x + 10 ) = ( y + 10 ) 5 .
⇒ 7x + 70 = 5y + 50 .
⇒ 7x + 70 - 50 = 5y
⇒ 7x + 20 = 5y. ........( 2 ).
Put value of 'x' from equation ( 1 ) in ( 2 ) .
⇒ 7× 3y/5 + 20 = 5y .
⇒ ( 21y + 100 ) / 5 = 5y .
⇒ 21y + 100 = 25y .
⇒ 100 = 25y - 21y =0
⇒ 100 = 4y .
⇒ 100 / 4 = y .
∴ y = 25
Therefore ,
∵ y = 25 ,
Put y = 25 in equation ( 1 ), we get
⇒ x = 3 × 25 / 5
⇒ x = 3 ×5
∴ x = 15
Original numbers are x and y = 15 and 25 .
Answer:
15 and 25
Step-by-step explanation:
Let the original number be x and y.
Given that, x : y = 3 : 5 ...( 1 )
Also, x + 5 : y + 5 = 2 : 3 ...( 2 )
From the first equation we get,
⇒ x/y = 3/5
⇒ x = 3y/5
Substituting this in the second equation we get,
⇒ ( 3y/5 ) + 5 / y + 5 = 2 / 3
Cross multiplying we get,
⇒ 3 [ (3y/5 ) + 5 ] = 2 ( y + 5 )
⇒ 9y/5 + 15 = 2y + 10
⇒ 2y - 9y/5 = 15 - 10
⇒ ( 10y - 9y ) / 5 = 5
⇒ y/5 = 5
⇒ y = 25
Therefore x is calculated as:
⇒ x = 3y/5
⇒ x = ( 3 × 25 ) / 5
⇒ x = 75/5 = 15
Hence the original numbers were 15 and 25.