There are five members A, B, C, D and E in a family. Ratio of ages of A and B five years ago was 3:4. Sum of ages of D and E five years hence will be 90. If Cwere born four years later than his actual date of birth, present Age of C would be half to that of present age E.
What is the age of D four years ago, if the current age of C is 27 years?

Options

A. A)36 years
B. B)34 years
C. C)38 years
D. D)30 years

Answer

To solve the problem step by step, let's break down the information given and find the required age of D four years ago.

### Step 1: Understand the current age of C
We are given that the current age of C is 27 years.

### Step 2: Determine the relationship between the ages of C and E
According to the problem, if C were born 4 years later than his actual date of birth, his age would be half of E's current age. This can be expressed mathematically as:
\[ 27 - 4 = \frac{E}{2} \]
This simplifies to:
\[ 23 = \frac{E}{2} \]
Multiplying both sides by 2 gives:
\[ E = 46 \]

### Step 3: Use the information about D and E's ages in the future
We know that the sum of the ages of D and E five years from now will be 90. This can be expressed as:
\[ (D + 5) + (E + 5) = 90 \]
Simplifying this gives:
\[ D + E + 10 = 90 \]
Thus:
\[ D + E = 80 \]

### Step 4: Substitute the value of E
Now, we substitute the value of E we found:
\[ D + 46 = 80 \]
Solving for D gives:
\[ D = 80 - 46 = 34 \]

### Step 5: Calculate the age of D four years ago
To find the age of D four years ago, we subtract 4 from D's current age:
\[ D - 4 = 34 - 4 = 30 \]

### Conclusion
The age of D four years ago is **30 years**.