# Difficult Percentages Solved QuestionAptitude Discussion

 Q. Peter got $30%$ of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got $40%$ of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?
 ✖ A. 35 ✖ B. 250 ✖ C. 75 ✔ D. 85

Solution:
Option(D) is correct

Let $x$ be the maximum marks in the examination.

Therefore, Peter got $30\%$ of $x$

$=\dfrac{30}{100}\times x$

$=0.3x$

And Paul got $40\%$ of $x$

$=\dfrac{40}{100}\times x$

$=0.4x$

In terms of the maximum marks Paul got $0.4x-0.3x = 0.1x$ more than Peter. --------(1)

The problem however, states that Paul got 15 marks more than the passing mark and Peter got 10 marks less than the passing mark.

Therefore, Paul has got 15 + 10 = 25 marks more than Peter.-------- (2)

Equating (1) and (2), we get

$0.1x=25$

$\Rightarrow x=250$

$x$ is the maximum mark and is equal to 250 marks.

We know that Peter got $30\%$ of the maximum marks.

Therefore, Peter got

$=\dfrac{30}{100}\times 250$

$=75$ marks

We also know that Peter got 10 marks less than the passing mark.

Therefore, the passing mark will be 10 marks more than what Peter got = $75 + 10 = 85$

Edit: For a shortcut alternative method, check comment by Chirag Goyal.

## (4) Comment(s)

Sikandar Naeem
()

Let passing marks = X

X = 30 % marks + 10

X + 15= 40 % marks ------------(i)

put value of x in equation i.

30 % +10 + 15 = 40 %

25 = 40%-30%

25 = 10%

total marks = 25/10% => 250

now passing marks (X) = (250 * 0.30) + 10

X= 85 RS

Supriya
()

Peter got 30 percent of max(let max marks be x)--> (30/x)*100,

Paul got 40 percent of total --->(40/x)*100

let the passing marks be P

so, (30/x)*100=P-10----(1)

and (40/x)*100=P+15----(2)

equate and find P

Sudarsanakapoor
()

simple short cut

pet Pa

30+10 40-15

differents

10----------25

100----------- ?( 250)--(total marks)

now pass percentage

30/100*250+10= 85

Chirag Goyal
()

$\text{% Difference of Max. Marks}$ $= \text{Difference in Obtained Marks Individually}$

$10 \text{ % of }x = 15 - (-10)$

$\Rightarrow x=250$

Passing Marks $= 30 \text{ % of } 250 + 10 = 85$