In the given questions two quantities are given one as quantity I and another as quantity II you have to determine relationship between two quantities choose appropriate option
Sohan and Mohan both get certain amount as pocket money. Both of them spend 40% of their pocket money. Sohan keeps 2/3rd and mohan 4/5th in their account of the remaining money. Difference between the amounts they keep in their bank account is 2400 rs.
quantityI:sohan's pocket money if mohan's pocket money is 25% more than sohan
quantityII:12000rs.

Options

A. `IltII`
B. `IgtII`
C. `IleII`
D. `I=II`

Answer

To solve the problem step by step, we will analyze the information given about Sohan and Mohan's pocket money and their savings.

### Step-by-Step Solution:

1. **Define Variables:**
Let Sohan's pocket money be \( X \) rupees. Since Mohan's pocket money is 25% more than Sohan's, we can express Mohan's pocket money as:
\[ \text{Mohan's pocket money} = X + 0.25X = 1.25X \]

2. **Calculate the Amount Spent:**
Both Sohan and Mohan spend 40% of their pocket money. Therefore, the amount they each have left after spending is:
\[ \text{Sohan's remaining money} = X - 0.4X = 0.6X \]
\[ \text{Mohan's remaining money} = 1.25X - 0.4(1.25X) = 1.25X - 0.5X = 0.75X \]

3. **Calculate the Amount Saved in the Bank:**
Sohan keeps \( \frac{2}{3} \) of his remaining money in the bank:
\[ \text{Sohan's savings} = \frac{2}{3} \times 0.6X = \frac{1.2X}{3} = 0.4X \]
Mohan keeps \( \frac{4}{5} \) of his remaining money in the bank:
\[ \text{Mohan's savings} = \frac{4}{5} \times 0.75X = \frac{3X}{5} \]

4. **Set Up the Equation for the Difference:**
We know the difference between the amounts they keep in their bank accounts is 2400 rupees:
\[ \left| \frac{3X}{5} - 0.4X \right| = 2400 \]

5. **Simplify the Equation:**
To simplify, we convert \( 0.4X \) to a fraction with a common denominator:
\[ 0.4X = \frac{2X}{5} \]
Now, substituting this into the equation gives:
\[ \left| \frac{3X}{5} - \frac{2X}{5} \right| = 2400 \]
This simplifies to:
\[ \left| \frac{X}{5} \right| = 2400 \]

6. **Solve for \( X \):**
Multiply both sides by 5 to isolate \( X \):
\[ X = 2400 \times 5 = 12000 \]

7. **Conclusion:**
Sohan's pocket money \( X \) is 12000 rupees.

### Comparison of Quantities:
- **Quantity I:** Sohan's pocket money = 12000 rupees.
- **Quantity II:** 12000 rupees.

Since both quantities are equal, we conclude that:

**Final Answer:** Quantity I is equal to Quantity II.