Tips and tricks and shortcuts on Percentage

• Here, are quick and easy tips and tricks on PrepInsta page for Percentage problems swiftly, easily, and efficiently in competitive exams and other recruitment exams.
• If the value of an item goes up or down by x%, the percentage reduction or increment to be now made to bring it back to the original point is $\mathbf{\frac{x}{100 + x } × 100 }$ %
• If A is x% more or less than B, then B is $\mathbf{\frac{x}{100 + x } × 100 }$ % less or more than A.
• If the price of an item goes up/down by x %, then the quantity consumed should be reduced by $\mathbf{\frac{x}{100 + x } × 100 }$ % so that the total expenditure remains the same.

Percentage – Ratio Equivalence table

Question 1. How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?

Options

A. 70 litre

B. 45 litre

C. 80 litre

D. 90 litre

Solution :

Let x liters of 20% alcohol solution,
Hence
$\implies 30\% = \frac{\text{x of 20% + 40 of 50%}}{x + 40}$
$\implies \frac{30}{100} = \frac{x \times \frac{20}{100} + 40 \times \frac{50}{100}}{x + 40}$
⇒ 20x+2000=30(x+40)
⇒ 20x+2000=30x+1200
⇒ 10x=800
⇒ x=80
∴ Required answer is 80 liters.

Correct option: C

Question 1. If the numerator of a fraction is increased by 20% and the denominator is decreased by 10%, then the value of the fraction is $\frac{16}{21}$ . What is the original fraction?

Options

A. $\frac{4}{5}$

B. $\frac{3}{5}$

C. $\frac{4}{7}$

D. $\frac{5}{7}$

Solution :

Let original fraction be $\frac{x}{y}$
According to the question,
Then from the given condition, $\frac{\text{x + 20% of x}}{\text{y-10% of y}} = \frac{16}{21}$
${\frac{x + \frac{x}{5}}{y - \frac{y}{10}} = \frac{16}{21}}$ ${\frac{\frac{6x}{5}}{\frac{9y}{10}} = \frac{16}{21}}$
$\implies \frac{x}{y} = \frac{16}{21} \times \frac{9}{10} \times \frac{5}{6} = \frac{4}{7}$

Correct option: C

Question 1. Ajay spends 50% of his salary and saves Rs. 500 per month. Find his monthly salary.

Options

A. 1000

B. 800

C. 600

D. 850

Solution :

Let the salary of Ajay be x
He spends 50% which means he saves 50% of the salary.
50% of x = 500
$\frac{50}{100}x = 500$
$x = 500 × \frac{100}{50}$
$x = \frac{50000}{50}$
x = 1000
Therefore, his monthly salary = 1000

Correct option: A

Question 1. The cost price of 20 chairs is the same as the selling price of x tables. If the profit is 25%, then find the value of x?

Options

A. 13

B. 18

C. 16

D. 12

Solution :

Let the CP of each chair = 1
Therefore CP of x table = x
20 CP = x SP
Profit % = SP/CP
1.25=20/x
x = 16

Correct option: C

Question 1. If $ 20\% $ of a = b, then b% of 20 is the same as:

Options

A. 5% of a

B. 4% of a

C. 8% of a

D. 2% of a

Solution :

20% of a = b
$\frac{20}{100} a = b$
b% of $20 =\frac{b}{100} × 20 = \frac{20}{100} × \frac{20}{100} × a$
= 4% of a

Correct option: B