Present average age of Kanika and Shweta is ‘x’ years. Ratio of the age of Kanika one year ago to the age of Monika four year hence will be 1: 2. Present average age of Kanika, Monika and Shweta is 22 years. Find the value of ‘x’ if the present age of Kanika is 16 yearsa)28 yearsb)26 yearsc)24 yearsd)20 yearsCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Given information:
- The present average age of Kanika and Shweta is 'x' years.
- The ratio of the age of Kanika one year ago to the age of Monika four years hence will be 1:2.
- The present average age of Kanika, Monika, and Shweta is 22 years.
- The present age of Kanika is 16 years.

To find: The value of 'x'.

Let's solve the problem step by step:

Step 1: Find the age of Kanika one year ago.
Since the present age of Kanika is 16 years, her age one year ago would be 16 - 1 = 15 years.

Step 2: Find the age of Monika four years hence.
Let the age of Monika four years hence be y years.
According to the given ratio,
(15 / y) = 1 / 2
Cross-multiplying,
2 * 15 = y
y = 30

Step 3: Find the sum of the present ages of Kanika, Monika, and Shweta.
The present average age of Kanika, Monika, and Shweta is 22 years.
Therefore, the sum of their present ages is 22 * 3 = 66 years.

Step 4: Find the present age of Shweta.
Since the sum of the present ages of Kanika, Monika, and Shweta is 66 years, and the present age of Kanika is 16 years, we can calculate the present age of Shweta as follows:
16 + Shweta's age = 66
Shweta's age = 66 - 16
Shweta's age = 50 years

Step 5: Find the present average age of Kanika and Shweta.
The present average age of Kanika and Shweta is 'x' years.
Therefore, (16 + 50) / 2 = x
66 / 2 = x
x = 33

Hence, the value of 'x' is 33.

Therefore, the correct answer is option 'D' (20 years)

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