Question

A student multiplied by 3/5 instead of 5/3. The percentage error in the calculation?

Answer 1

A student multiplied by 3/5 instead of 5/3.

Let a number is x.

now, correct calculation = 5x/3

wrong calculation = 3x/5

so, change in calculation = correct calculation - wrong calculation

= 5x/3 - 3x/5 = (25x - 9x)/15 = 16x/15

now, % error in calculation = change in calculation/correct calculation × 100

= (16x/15)/(5x/3) × 100

= (16x × 3)/(15 × 5x) × 100

= (16)/(25) × 100

= 16 × 4

= 64

hence, percentage error in the calculation is 64%