two numbers are such that the ratio between them is three to five. when ten is added to the numbers, the ration becomes five to seven. What are the original numbers?
Answers
To Find:
- Two original numbers.
Answer:
→ x = 15 and y = 25 .
Solution:
Let, x and y be the two numbers
Now,
✔️ CASE 1:
→ Two numbers are such that the ratio between them is 3:5
According to the Qusetion,
∵ 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
According to the Qusetion,
∵ ( 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
⇒ 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 = 15 and y = 25
Hence,
It is solved.
Step-by-step explanation:
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