Ankit is 5 times as heavy as Suraj. Suraj is one third the weight of Imran. Imran is 4/3 times as heavy as Shrey. Shrey is half the weight of Gagan. Who is the lightest?

Options

A. Imran
B. Shrey
C. Suraj
D. Suraj or Shrey

Answer

To solve the problem step by step, we will define the weights of each person using variables and then relate them according to the information given in the question.

### Step 1: Define Suraj's Weight
Let the weight of Suraj be \( X \).

### Step 2: Calculate Ankit's Weight
According to the problem, Ankit is 5 times as heavy as Suraj. Therefore, Ankit's weight will be:
\[ \text{Weight of Ankit} = 5X \]

### Step 3: Calculate Imran's Weight
Suraj is one third the weight of Imran. This means:
\[ \text{Weight of Imran} = 3 \times \text{Weight of Suraj} = 3X \]

### Step 4: Calculate Shrey's Weight
Imran is \( \frac{4}{3} \) times as heavy as Shrey. Therefore, we can express Shrey's weight as:
\[ \text{Weight of Shrey} = \frac{3}{4} \times \text{Weight of Imran} = \frac{3}{4} \times 3X = \frac{9X}{4} \]

### Step 5: Calculate Gagan's Weight
Shrey is half the weight of Gagan. Thus, we can express Gagan's weight as:
\[ \text{Weight of Gagan} = 2 \times \text{Weight of Shrey} = 2 \times \frac{9X}{4} = \frac{18X}{4} = \frac{9X}{2} \]

### Step 6: Compare All Weights
Now we have the weights expressed in terms of \( X \):
- Suraj: \( X \)
- Ankit: \( 5X \)
- Imran: \( 3X \)
- Shrey: \( \frac{9X}{4} \)
- Gagan: \( \frac{9X}{2} \)

### Step 7: Determine the Lightest
To find the lightest person, we compare the coefficients:
- \( X \) (Suraj)
- \( 5X \) (Ankit)
- \( 3X \) (Imran)
- \( \frac{9X}{4} \) (Shrey)
- \( \frac{9X}{2} \) (Gagan)

Among these, \( X \) (Suraj) is the smallest value.

### Conclusion
Thus, the lightest person is **Suraj**.