Q3

Number Theory Level 2

A person was asked what is 16 17 \frac{16}{17} of a certain fraction. By mistake he divided the fraction by 16 17 \frac{16}{17} and got an answer, which exceeds the correct answer by 33 340 \frac{33}{340} . The correct answer is :

This question is a part of my set NMTC 2015
62 85 \frac{62}{85} 60 87 \frac{60}{87} 67 85 \frac{67}{85} 64 85 \frac{64}{85}

Satyajit Ghosh by Satyajit Ghosh , 21, India

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1 solution

Denton Young
Aug 26, 2015

The incorrect answer is 17 / 16 ∗ 17 / 16 = 289 / 256 17/16 * 17/16 = 289/256 the correct answer, so the difference between the two is ( 289 − 256 ) / 256 = 33 / 256 (289-256)/256 = 33/256 of the correct answer too high.

The amount it exceeds the correct answer by is 33 / 340 33/340 , so the correct answer is 33 / 340 33/340 divided by 33 / 256 = 256 / 340 33/256 = 256/340

Simplifying yields 64/85

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Hey. 16x/17+33/340=17x/16

Which gives x = 68/85

Raj kishore Agrawal - 5 years, 1 month ago

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