Aptitude - Percentage - Discussion

Error comes from true value so;.

Error% = error/true value.

Let number is 100.

Actual Multiplication = (100 *5)/3 = 500/3.
Student multiplied = (100 *3)/5 = 300/5.

Error,

= (500/3) - (300/5),
= (2500 - 900)/15,
= 1600/15.
%Error = (1600 *100 *3)/(15*500) = 64%.

Let's assume no is 30 it is divisible by both 5 and 3 ,and not get fractions.

No = 30.
3/5 * 30 =18
5/3 * 30 = 50
Error means = (difference/correct value ) * 100
Error = 32/50*100
Ans = 64.

Let, X be the exact value.
And Y be the error value.

Now, the formula for percentage error= (X-Y)/X *100%
{(5/3-3/5)÷5/3}*100%.
= (16/15*3/5)*100%,
= 64%.

In this question, take LCM of denominators of fractions 3/5 & 5/3 ( to make the calculation easier).

As the denominators are 5 & 3,
LCM is 15.

Now
Mistaken value = 15 * (3/5) = 9,
True value = 15 * (5/3)= 25.

Error = ( True value - mistaken value )/( true value),
= (25 - 9)/ 25 = 16/25,

Error %= Error * 100.
= (16/25)* 100.
= 64%.

Hope this helps.

How 16/15 came? Please explain.

Lets take the number is 15.

Correct value is 5/3*15 = 25.
The error value is 3/5 * 15 = 9,
The difference is 11,
So 11/25*10 = 64.

Hey take suppose a number 10 and multiply with 3/5 i.e >3/5*10=6, and the same number 10 is multiplied by 5/3.

i.e >5/3*10=16. 6=~17 then get the difference from each 17-6=11 then to find the real value and fake value.

Real value =17 anf the fake value =6.

So, we have the task to find the difference values percentage over the real value i.e >17 is 100% then 11 (difference value) is what percentage of 17 =64%.

Thank you @Srihari.

Here, I use ratio and proportion. The question states using a number of some value and multiplying by 3/5 and 5/3. what is the difference in percentage?

3/5 = 60%. 5/3 = 166.6%.
The percentage difference is arguably 107%. If you use a predetermined value of 10.
The equations are 3/5 x 10 = .6 and 5/3 x 10 = 1.66. The calculated % is 1.66/.6 = 2.76 or 276%.
This is the true difference in % values no matter what number you multiply them by. 276% x 0.6 = 1.66.