If 35 is subtracted from a number, reduces to its 80%. What is $\left( \frac{4}{5} \right)$ th of that number ?

Question

Accepted Answer

To solve the problem, we need to determine the original number based on the given condition and then find $\left( \frac{4}{5} \right)$th of that number.

**Step-by-step Explanation:**

1. **Understanding the Condition:**
   - We are given that if 35 is subtracted from a number, it reduces to 80% of that number.
   - Let the original number be $ x $.
   - According to the condition: $ x - 35 = 0.8x $.

2. **Solving the Equation:**
   - Rearrange the equation: $ x - 0.8x = 35 $.
   - Simplify: $ 0.2x = 35 $.
   - Solve for $ x $: $ x = \frac{35}{0.2} = 175 $.

3. **Finding $\left( \frac{4}{5} \right)$th of the Number:**
   - We need to find $\left( \frac{4}{5} \right)$th of 175.
   - Calculation: $\left( \frac{4}{5} \right) \times 175 = \frac{4 \times 175}{5} = \frac{700}{5} = 140$.

4. **Conclusion:**
   - Therefore, $\left( \frac{4}{5} \right)$th of the original number is 140.

**Explanation of Why Other Options are Incorrect:**

- **Option 1 (70):** 
  - If $\left( \frac{4}{5} \right)$th of the number were 70, then the original number would be $ \frac{70 \times 5}{4} = 87.5 $, which does not satisfy the condition $ x - 35 = 0.8x $.

- **Option 2 (90):**
  - If $\left( \frac{4}{5} \right)$th of the number were 90, then the original number would be $ \frac{90 \times 5}{4} = 112.5 $, which does not satisfy the condition $ x - 35 = 0.8x $.

- **Option 3 (120):**
  - If $\left( \frac{4}{5} \right)$th of the number were 120, then the original number would be $ \frac{120 \times 5}{4} = 150 $, which does not satisfy the condition $ x - 35 = 0.8x $.

Thus, Option 4 (140) is the only correct answer, as it aligns with the given condition and calculations.