CAT 2025 Lesson : Percentages - Past Questions

Observation/Strategy
1) We can assume values as there are no absolute values given.
2) The new breadth and height need to be halved. So, will help if their assumed values are a multiple of 2.
3) The ratio of assumed values of $l$, $b$ and $h$ should be $3 : 2 : 1$

Lets assume length ($l$), breadth ($b$), and height ($h$) are $6$, $4$ and $2$ respectively.

There are two walls along the length and two walls along the breadth.

Original area of the four walls = $2lh$ + $2bh$
$= 2 \times 6 \times 2 + 2 \times 4 \times 2 = \bm{40}$

New $l$, $b$ and $h$ are $12$, $2$ and $1$ respectively.

New area of the four walls $= 2 \times 12 \times 1 + 2 \times 2 \times 1 = \bm{28}$

Change in area = $\dfrac{28 - 40}{40} \times 100\% = -30\%$

Answer: (5) decrease by $30\%$

Observation/Strategy
1) We can assume values as there are no absolute values given.
2) As ratio of male to female is $5 : 4$, will help if the total value is a multiple of $9$.
3) As $30\%$ of male and $40\%$ of female are to be found, will help if number of males and females are multiples of $10$.
4) Newspaper has exactly two sections - political and sports.

Let the total number of journalists be $90$. Number of male and female journalists is $50$ and $40$ respectively.

Journalists covering political news = $\dfrac{30}{100} \times 50 + \dfrac{40}{100} \times 40 = 31$

Journalists covering Sports news = $90 - 31 = 59$

Sports journalists as $\%$ of total = $\dfrac{59}{90} \times 100\% = \dfrac{590}{9}\% = 65.56\%$

Answer: (1) $65$ percent

Observation/Strategy
1) We can assume values as there are no absolute values given.
2) Prices are always equal and talktimes are compared.
3) Comparison is between two service providers - Airtel and Vodafone.
4) Each of the companies have two types of recharges - pre-paid and post-paid.
5) We can form a $2 \times 2$ table and then fill the values (to avoid silly mistakes).

Let the talktime on pre-paid recharge of Vodafone be $100$. Pre-paid of Airtel is $21\%$ less at $79$.

Type	Prepaid	Postpaid
Vodafone	$100$
Airtel	$79$

Post-paid of Airtel = $1.12 \times 79 \sim 88.5$

Post-paid of Vodafone = $0.85 \times 100 = 85$

Type	Prepaid	Postpaid
Vodafone	$100$	$85$
Airtel	$79$	$88.48$

“Post-paid Airtel talktime is $x\%$ less/more than post-paid Vodafone” is the statement. Note that comparison is with Vodafone post-paid.

$x = \dfrac{88.5 - 85}{85} \times 100\%$

$= \dfrac{70}{17}\% \sim 4.1\%$

Note that none of the options are correct here.

$\therefore$ Closest option of $3.9\%$ more is deemed to be correct.

Answer: (1) $3.9\%$ more

Note: Kindly remember to choose the closest option when none of the options have the actual answer and 'None of the Above' is not in the answer options.