Question:
A student instead of finding the value of \(\frac{7}{8}\) of a number, found the value of \(\frac{7}{18}\) of the number. If his answer differed from the actual one by 770, find the number.
A student instead of finding the value of \(\frac{7}{8}\) of a number, found the value of \(\frac{7}{18}\) of the number. If his answer differed from the actual one by 770, find the number.
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Write the difference \(\frac{7}{8}x - \frac{7}{18}x\) and equate it to 770.
Updated On: Nov 4, 2026
- 2520
- 1584
- 1728
- 1656
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The Correct Option is B
Solution and Explanation
Step 1: Set up:
Let the number be x. Then \(\frac{7}{8}x - \frac{7}{18}x = 770\).
Step 2: Simplify:
\(7x\left(\frac{1}{8} - \frac{1}{18}\right) = 7x \cdot \frac{9-4}{72} = \frac{35x}{72}\).
Step 3: Solve:
\(\frac{35x}{72} = 770 \Rightarrow x = \frac{770 \times 72}{35} = 22 \times 72 = 1584\).
Final Answer:
The correct option is (2): 1584
Let the number be x. Then \(\frac{7}{8}x - \frac{7}{18}x = 770\).
Step 2: Simplify:
\(7x\left(\frac{1}{8} - \frac{1}{18}\right) = 7x \cdot \frac{9-4}{72} = \frac{35x}{72}\).
Step 3: Solve:
\(\frac{35x}{72} = 770 \Rightarrow x = \frac{770 \times 72}{35} = 22 \times 72 = 1584\).
Final Answer:
The correct option is (2): 1584
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