Maintaining the ratio

Number Theory Level 1

Robert solved some fraction problems on Brilliant and we have the following information.

  1. He attempted only 9 10 \frac{9}{10} of all the problems.
  2. He answered correctly only to 9 10 \frac{9}{10} of the attempted problems.

If he answered incorrectly to 18 problems, how many problems were there in all?


The answer is 200.

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Mohammad Farhat
Aug 17, 2018

He only attempted 9 10 \dfrac{9}{10} of the problems

Multiply 9 10 \dfrac{9}{10} by 9 10 \dfrac{9}{10} . We get 81 100 \dfrac{81}{100}

We know that 9 10 \dfrac{9}{10} = 90 100 \dfrac{90}{100}

Subtract 81 100 \dfrac{81}{100} from 90 100 \dfrac{90}{100} . We get 9 100 \dfrac{9}{100} .

Given that 9 100 \dfrac{9}{100} = 18 problems

Dividing each side by 9, we get 1 100 \dfrac{1}{100} = 2 problems

Multiplying each side by 100, we get 100 100 \dfrac{100}{100} which is 1 = 200 problems

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@Sandeep Bhardwaj , How do I join your classes? I really want to.

Mohammad Farhat - 2 years, 8 months ago

@Sandeep Bhardwaj , Can you please reply?

Mohammad Farhat - 2 years, 8 months ago

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