Question

Student multiplied a number by 5/3 instead of 3/5. What is percentage error in calculations.

Answer 1

Let a number is x .

ideally, student should have multiplied x by 3/5 .

hence, the correct result was x × 3/5 = 3x/5

by mistake, he multiplied x by 5/3

hence, the incorrect result was x × 5/3 = 5x/3

error = incorrect result - correct result

= (5x/3 - 3x/5)

= (25x - 9x)/15

= 16x/15

percentage error = error/correct value × 100

= (16x/15)/(3x/5) × 100

= 16x × 5/(15 × 3x) × 100

= 1600/9 = 177.77%

Answer 2

Answer:

Let the number be x.

Then , when multiplied by 5/3, the number becomes (5/3)x. This is the value obtained by mistake by the student.

When multiplied by 3/5, the number becomes (3/5)x.

Percentage error = [(5/3)x - {(3/5)x] / (3/5)x } * 100

= [ (16/15) / (3/5) ] * 100

= (16/9) * 100

= 177.7 %

Therefore, the percentage error is 177.7%.