The ratio of the age of Ram and Shyam 15 years ago was 2 : 5. The ratio of their present ages is 5 : 8. What will be the present age of Shyam?a)10b)15c)25d)40Correct answer is option 'D'. Can you explain this answer?

Question

Answer

D

Answer

GIVEN:
Ratio of age of Ram and Shyam (15 years ago)= 2 : 5
Ratio of present age of Ram and Shyam = 5 : 8

CALCULATION:
Let the ages of Ram and Shyam be x and y respectively.
⇒ x ∶ y = 5 ∶ 8
⇒ x/y = 5/8
⇒ x = 5y/8 ----(1)
Now, 15 years ago the ratio was 2 ∶ 5
⇒ (x - 15) / (y - 15) = 2/5
⇒ 5x – 2y = 45
⇒ 5(5y/8) – 2y = 45 from (1)
∴ y = 360/9 = 40 years.

Answer

GIVEN:
Ratio of age of Ram and Shyam (15 years ago)= 2 : 5
Ratio of present age of Ram and Shyam = 5 : 8

CALCULATION:
Let the ages of Ram and Shyam be x and y respectively.
⇒ x ∶ y = 5 ∶ 8
⇒ x/y = 5/8
⇒ x = 5y/8 ----(1)
Now, 15 years ago the ratio was 2 ∶ 5
⇒ (x - 15) / (y - 15) = 2/5
⇒ 5x – 2y = 45
⇒ 5(5y/8) – 2y = 45 from (1)
∴ y = 360/9 = 40 years.

Answer

GIVEN:
Ratio of age of Ram and Shyam (15 years ago)= 2 : 5
Ratio of present age of Ram and Shyam = 5 : 8

CALCULATION:
Let the ages of Ram and Shyam be x and y respectively.
⇒ x ∶ y = 5 ∶ 8
⇒ x/y = 5/8
⇒ x = 5y/8 ----(1)
Now, 15 years ago the ratio was 2 ∶ 5
⇒ (x - 15) / (y - 15) = 2/5
⇒ 5x – 2y = 45
⇒ 5(5y/8) – 2y = 45 from (1)
∴ y = 360/9 = 40 years.

Answer

Given:
The ratio of the age of Ram and Shyam 15 years ago was 2:5.
The ratio of their present ages is 5:8.

To find:
The present age of Shyam.

Solution:
Let's assume that the present age of Ram and Shyam is 5x and 8x respectively.

Ratio of their ages 15 years ago:
15 years ago, the age of Ram would be 5x - 15 and the age of Shyam would be 8x - 15.
According to the given ratio, (5x - 15) / (8x - 15) = 2/5.

Cross-multiplying:
5(5x - 15) = 2(8x - 15)
25x - 75 = 16x - 30

Simplifying the equation:
25x - 16x = 75 - 30
9x = 45
x = 45/9
x = 5

Present age of Shyam:
Since the present age of Shyam is 8x, substituting the value of x, we get:
Present age of Shyam = 8 * 5 = 40.

Therefore, the present age of Shyam is 40 years (option D).

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