Tips And Tricks And Shortcuts of Percentage

Type 1: Percentage Tips and Tricks and Shortcuts- Based on Mixtures and Alligation

Question 1. A small container has 60l of milk and water mixture. It was made by mixing milk and water in which 80% is milk. Rohan came and added some water in the mixture. Now, find out how much water was added to the mixture that the percentage of milk became 60%?

Options:

A. 20 litre

B. 25 litre

C. 2 litre

D. 10 litre

Solution:     Given, percentage of milk = 80%

It means, the percentage of water = 20%

In 60L of mixture, water = \frac{60 × 20 }{100} = \frac{1200 }{100} = 12 litre

Let the water added = x

Now, \frac{12 + x }{60 + x}× 100 = 40 (it is because in the new mixture milk is 60%, 100 – 60 = 40% water)

1200 + 100x = 2400 + 40x

100x – 40x = 2400 – 1200

60x = 1200

x= 20 litre

Correct option: A

Type 2: Percentage Tips and Tricks – Problems based on Ratios and Fractions

Question 1. If the numerator of a fraction is increased by 50% and the denominator is decreased by 10%, the value of the new fraction becomes \frac{4}{5} . Find the original fraction?

Options:

A. \frac{12}{21}

B. \frac{13}{20}

C. \frac{12}{25}

D. \frac{25}{12}

Solution:     Let original numerator be x

Let original denominator be y

Let original fraction be \frac{x}{y}

According to the question,

Numerator of a fraction is increased by 50% = \frac{150}{100x}

Denominator is decreased by 10% = \frac{90}{100}

Now, \frac{\frac{150}{100} x }{  \frac{90}{100} y}= \frac{4}{5}

\frac{150x}{90y} =\frac{4}{5}

\frac{x}{y}= \frac{4}{5} × \frac{90}{150}= \frac{12}{25}

Correct option: C