Question

If two numbers are in the ratio of 3:5 If 12 is added to both the numbers then the ratio becomes 5:7. The sum of the given two numbers is?
48
56
32
40​

Answer 1

Required Answer:-

Given:

• Two numbers are in the ratio of 3 : 5.
• If 12 is added to both the numbers, then the ratio becomes 5 : 7.

To Find:

• The sum of the numbers.

Solution:

Let the numbers be 3x and 5x.

On Adding 12, numbers become 3x + 12 and 5x + 12

According to the given condition,

➡ (3x + 12)/(5x + 12) = 5/7

➡ 7(3x + 12) = 5(5x + 12)

➡ 21x + 84 = 25x + 60

➡ 4x = 24

➡ x = 6

Hence,

➡ 3x = 18

➡ 5x = 30

So, the numbers are 18 and 30

Therefore, sum of the numbers will be,

= 18 + 30

= 48

★ Hence, 48 is the right answer for the question.

Verification:

Numbers are - 18 and 30

Ratio = 18/30 = 3 : 5

Adding 12, we get the numbers - 30 and 42.

Ratio = 30/42 = 5 : 7.

Hence, our answer is correct (Verified)

Answer 2

Given :-

• If two numbers are in the ratio of 3:5 If 12 is added to both the numbers then the ratio becomes 5:7.

To Find :-

• The sum of the given two numbers.

Solution :-

⟼ Let the First Number be 3x

⟼ Let the Second Number be 5x

After adding 12 to both the Numbers :

⟼ Let the First Number be 3x + 12

⟼ Let the Second Number be 5x + 12

According to the Question :

⟹ (3x + 12) / (5x + 12) = 5/7

⟹ 7 (3x + 12) = 5 (5x + 12)

⟹ 21x + 84 = 25x + 60

⟹ 84 - 60 = 25x - 21x

⟹ 84 - 60 = 4x

⟹ 24 = 4x

⟹ 24/4 = x

⟹ 6 = x

________________

⟾ First Number = 3x

⟾ First Number = 3 × 6

⟾ First Number = 18

⟾ Second Number = 5x

⟾ Second Number = 5 × 6

⟾ Second Number = 30

________________

Sum of Obtained Numbers :-

⟹ 18 + 30

⟹ 48

Therefore, Correct Option is A i.e 48

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