If P is 15 years old now Q will be 26 years old after 6 year what is the ratio of their present ages?

Options

A. `4:1`
B. `3:4`
C. `2:1`
D. `2:3`

Answer

To solve the problem step by step, we will determine the present ages of P and Q, and then find the ratio of their ages.

### Step 1: Determine P's Present Age
- We are given that P is currently 15 years old.

### Step 2: Determine Q's Present Age
- We know that Q will be 26 years old after 6 years.
- To find Q's present age, we subtract 6 years from 26 years:
\[ Q's \, present \, age = 26 - 6 = 20 \, years \]

### Step 3: Find the Ratio of Their Present Ages
- Now that we have both present ages:
- P's age = 15 years
- Q's age = 20 years
- The ratio of their present ages can be expressed as:
\[ \text{Ratio} = \frac{P's \, age}{Q's \, age} = \frac{15}{20} \]

### Step 4: Simplify the Ratio
- To simplify the ratio \( \frac{15}{20} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
\[ \frac{15 \div 5}{20 \div 5} = \frac{3}{4} \]

### Final Answer
- Therefore, the ratio of their present ages is \( 3:4 \).

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