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Q.

Two integers are set up so that their ratio is 3 to 5. When each is increased by 10, the resultant numbers have a 5 to 7 ratio. Identify the initial numbers.


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a

12, 20

b

20, 12

c

25, 15

d

15, 25 

answer is D.

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Detailed Solution

Given that, two integers are set up so that their ratio is 3 to 5.
When each is increased by 10, the resultant numbers have a 5 to 7 ratio.
Let the two integers be 3n,5n  …. (i)
From given:
Adding 10 to both numbers, the new ration is 3n+10 5n+10 = 5 7  .
After cross-multiplication,
⇒7 3n+10 =5(5n+10) ⇒7(3n)+7(10)=5(5n)+5(10) ⇒21n+70=25n+50 ⇒21n−25n=50−70 ⇒−4n=−20 ⇒n= −20 −4 ⇒n=5  
Substituting value of n=5   in (i),
The two integers be,
⇒3n
⇒3(5)
⇒15
The other number is,
⇒5n
⇒3(5)
⇒25
Two integers are 15, 25.
Hence, option 4 is correct.
 
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Two integers are set up so that their ratio is 3 to 5. When each is increased by 10, the resultant numbers have a 5 to 7 ratio. Identify the initial numbers.