Question

linear equations

13. Two numbers are in the ratio 3:5. If each is increased by 10, the ratio between the new numbers
so formed is 5: 7. Find the original numbers.
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Answer 1

Answer:

let the numbers be 3x and 5x

then, according to the question :

3x + 10/5x + 10 = 5/7

=> 21x + 70 = 25x + 50

=> -4x = -20

=> X = 5.

so, 3x = 15

& 5x = 25

hence, the original numbers are 15 and 25.

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Answer 2

Answer:

Original numbers are 15 and 25.

Step-by-step explanation:

Given: Initial ratio of two number is 3:5

-Final ratio after increasing both numerator and denominator by 10 is 5:7

Step 1: Let the common multiple be x

Therefore, Numerator = 3x, Denominator = 5x

Step 2: Now 10 is added to both numerator and denominator

Hence, Numerator becomes (3x + 10)

and Denominator becomes (5x + 10)

Step 3: Equating ratio-

=> (3x+10)/(5x+10) =5/7

=> 21x+70=25x+50

=> 4x=20

=> x=5

Step 4: Hence, Original numbers are

Numerator=> 3x => 3×5=> 15

Denominator=> 5x=> 5×5=> 25

Solution: Original numbers are 15 and 25.