High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ A boy on being asked what \( \frac{16}{17} \) of a fraction was made the mistake of dividing the fraction by \( \frac{6}{7} \), and got an answer, which exceeded the correct answer by \( \frac{33}{340} \). The correct answer is:

(a) \( \frac{68}{85} \)
(b) \( \frac{65}{84} \)
(c) \( \frac{32}{40} \)
(d) None of these

Answer :

To solve the problem, we need to find the correct answer to the fraction problem and determine which given option matches this.

Step-by-step Explanation:


  1. Understanding the problem:


    • The boy made a mistake and instead of finding [tex]\frac{16}{17}[/tex] of a fraction [tex]x[/tex], he divided the fraction by [tex]\frac{6}{7}[/tex].

    • His incorrect answer exceeded the correct answer by [tex]\frac{33}{340}[/tex].



  2. Mathematical representation:


    • The correct operation should be [tex]\frac{16}{17} \times x[/tex].

    • The incorrect operation he performed is [tex]x \div \frac{6}{7} = x \times \frac{7}{6}[/tex].

    • Therefore, the incorrect answer is [tex]x \times \frac{7}{6}[/tex].



  3. Equation setup:


    • According to the problem, [tex]x \times \frac{7}{6} = \frac{16}{17} \times x + \frac{33}{340}[/tex].



  4. Simplifying and solving for [tex]x[/tex]:


    • Equating both sides:
      [tex]x \times \frac{7}{6} = \frac{16}{17} \times x + \frac{33}{340}[/tex]

    • Rearrange the equation:
      [tex]x \times \frac{7}{6} - \frac{16}{17} \times x = \frac{33}{340}[/tex]

    • Find a common factor for the left side, which involves rearranging terms:
      [tex]x \left( \frac{7}{6} - \frac{16}{17} \right) = \frac{33}{340}[/tex]

    • Equivalent fraction subtraction: [tex]\frac{7}{6} - \frac{16}{17}[/tex]

      • Find a common denominator: For [tex]6[/tex] and [tex]17[/tex] is [tex]102[/tex].

      • Convert: [tex]\frac{7}{6} = \frac{119}{102}[/tex] and [tex]\frac{16}{17} = \frac{96}{102}[/tex].

      • Subtract: [tex]\frac{119}{102} - \frac{96}{102} = \frac{23}{102}[/tex].





  5. Solving for [tex]x[/tex]:


    • Replace and solve: [tex]x \times \frac{23}{102} = \frac{33}{340}[/tex]

    • Multiply both sides by [tex]\frac{102}{23}[/tex] to isolate [tex]x[/tex]:
      [tex]x = \frac{33}{340} \times \frac{102}{23}[/tex]

    • Simplify:
      [tex]x = \frac{33 \times 102}{340 \times 23}[/tex]

    • Reduce by finding the GCD (Greatest Common Divisor) and simplifying:
      [tex]x = \frac{11 \times 6}{85 \times 1}[/tex]
      [tex]x = \frac{66}{85}[/tex]



  6. Choosing the correct option:


    • None of the options directly matches our result [tex]\frac{66}{85}[/tex].

    • Therefore, the answer is: (d) None of these.




This solution involves setting up an equation based on the erroneous calculation versus the correct calculation and solving for the unknown fraction [tex]x[/tex].

Other Questions