Question

Amreeshdar instead of finding the value of 7/8th of a number, found the value of 7/18th of the number. If his answer differed from the actual answer by 770, determine the number that Amreeshdar wanted to find?

• A. 1520
• B. 1584
• C. 1556
• D. 1656
• E. 1728

Hint:

When dealing with fractions of a number, set up an equation for the difference and solve for the unknown.

Answer 1

The Correct Option is B

Step 1: Let the number be $x$.
Step 2: Actual value = $\frac{7}{8}x$. Incorrect value = $\frac{7}{18}x$.
Step 3: Difference = $\frac{7}{8}x - \frac{7}{18}x = 770$.
Step 4: Factor: $7x\left(\frac{1}{8} - \frac{1}{18}\right) = 770$.
Step 5: $\frac{1}{8} - \frac{1}{18} = \frac{9-4}{72} = \frac{5}{72}$.
Step 6: So $7x \times \frac{5}{72} = 770 \implies \frac{35x}{72} = 770$.
Step 7: $35x = 770 \times 72 = 55440 \implies x = \frac{55440}{35} = 1584$.
Step 8: Final Answer: The number is 1584.