CAT 2025 Lesson : Percentages - Common Types

If Aparna has $15\%$ more mangoes than Bhavna, then Bhavna has ___$\%$ less mangoes than Aparna. Fill in the blank.

(1) $11\%$            (2) $13\%$            (3) $17\%$            (4) $19\%$           

Solution

Aparna has $\dfrac{15}{100} = \dfrac{3}{20}$ more mangoes than Bhavna.

∴ Bhavna has $\dfrac{3}{20 + 3} = \dfrac{3}{23}$ less mangoes than Aparna

As a percentage, $\dfrac{3}{23} = \dfrac{3}{23} \times$ 100% ~ 13%

Answer: (2) 13%

A store sells shirts at Rs. $810$, with a profit margin of $8\%$. What is the cost price of a shirt?

Solution

Where CP, SP and $p$ are the Cost Price, Selling Price and Profit $\%$, the formula for calculating SP is as follows.

$\text{CP} \times \left( 1 + \dfrac{p}{100} \right) = \text{SP}$

⇒ $\text{CP} \times \left( 1 + \dfrac{8}{100} \right) = 810$

⇒ $\text{CP} = 810 \times \dfrac{100}{108} = 750$

Answer: Rs. $750$

In May 2019, Albert spends 80% of his salary. The rest are his savings for the month. In the subsequent month, he receives a 20% increase in his monthly salary but his expenses for the month also increase by 30%. What was the percentage change in his savings in June 2019?

(1) $-10\%$            (2) $-20\%$            (3) $10\%$            (4) $20\%$           

Solution

As the question is only in percentage terms, we can assume values. Secondly, for the 2 months, we have expenses and savings. Therefore, we can use a table to fill details.

Let the salary in May 2019 be Rs. 100.
∴ Expenses and Savings in May 2019 are Rs. 80 and Rs. 20 respectively.

	May	June
Expense	80
Savings	20
Salary	100

Salary in June 2019 = $1.2 \times 100 = 120$
Expenses in June 2019 = $1.3 \times 80 = 104$
Savings in June 2019 = 120 - 104 = 16

	May	June
Expense	80	104
Savings	20	16
Salary	100	120

% change in savings in June 2019 = $\dfrac{16 -20}{20} \times$ 100% = - 20%

Answer: (2) –20%

Rs. $89,538$ was to be paid up as capital by the $4$ partners - P, Q, R and S. P paid $25\%$ of this amount. Q paid $20\%$ of the remainder. R's capital contribution was $4$ times that of S. If the requirement was exactly covered by these capital contributions, then what was the capital contribution of S?

(1) Rs. $8,754$            (2) Rs. $10,745$            (3) Rs. $12,342$            (4) Rs. $15,679$           

Solution

The total capital contribution of Rs. $89,538$ is a difficult figure to work with. Therefore, let's assume that the total capital is Rs. $100$.

P's capital = $\dfrac{25}{100} \times 100 = 25$

Q's capital = $\dfrac{20}{100} \times (100 - 25) = 15$

Capital of R and S = $100 - 25 - 15$ = Rs. $60$

Let the capital contribution of S be $x$. Then, that of R = $4x$.

$4x + x = 60$
⇒ $x = 12$

Where the total capital is Rs. $100$, S's contribution is Rs. $12$, which means S's contribution is $12\%$ of the total.

Capital brought in by S = $\dfrac{12}{100} \times 89538$

As the answer options are quite apart, we can round off 89538 to 90000.
$\dfrac{12}{100} \times 89538 \sim \dfrac{12}{100} \times 90000 = 10800$

The closest answer here is Rs. $10,745$.

Answer: (2) Rs. $10,745$

A class has $5$ students and all of them wrote a Science test. The test had $2$ parts - Physics and Chemistry. Rahul scored $30\%$ of the total marks scored by the entire class. $20\%$ of Rahul's marks came from Chemistry. If Rahul's marks in Physics was $40\%$ of the total marks scored by the entire class in Physics, then the ratio of marks scored in Chemistry by Rahul to that of the rest of the class is

(1) $3 : 17$            (2) $4 : 21$            (3) $7 : 23$            (4) $19 : 81$           

Solution

With no absolute values given, we can assume 100 as total marks scored by all students in the Science test.

Secondly, Rahul's marks are provided as a percentage of the entire class. As Physics and Chemistry marks are there for each, we can use a table to fill details.

Rahul's total marks = $\dfrac{30}{100} \times 100 = 30$

Rahul's marks in Chemistry = $\dfrac{20}{100} \times 30 = 6$

	Physics	Chemistry	Total
Rahul	24	6	30
Rest of the Class			70
Total			100

Rahul's marks in Physics is 40% of that of the entire class.

∴ Total Physics marks = $24 \times \dfrac{100}{40} = 60$

∴ Total Chemistry marks = 100 – 60 = 40

	Physics	Chemistry	Total
Rahul	24	6	30
Rest of the Class	36	34	70
Total	60	40	100

Ratio of Rahul's marks in Chemistry to that of the entire class = 6 : 34 = 3 : 17

Answer: (1) $3 : 17$