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# Ratio & Proportion

1.

In a bag, there are coins of $$25 p, 10 p$$ and $$5 p$$ in the ratio of $$1 : 2 : 3.$$ If there is $$Rs. 30$$ in all, how many $$5 p$$ coins are there?

Let the number of $$25 p, 10 p$$ and $$5 p$$ coins be $$x, 2x, 3x$$ respectively.

Then, sum of there value $$= Rs. (\frac{25x}{100} + \frac{10 \times 2x}{100} + \frac{5 \times 3x}{100}) = Rs. \frac{60x}{100}$$

$$\therefore \frac{60x}{100} = 30 \Leftrightarrow x = \frac{300 \times 100}{60} = 50.$$

Heance, the number of $$5 p$$ coins $$= (3 \times 50) = 150.$$

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2.

Two number are in the ratio $$3 : 5.$$ If $$9$$ is subtracted from each, the new numbers are in the ratio $$12 : 23.$$ The smaller number is:

Let the numbers be $$3x$$ and $$5x.$$

Then, $$\frac{3x - 9}{5x - 9} = \frac{12}{23}$$

$$\Rightarrow 23(3x - 9) = 12(5x - 9)$$

$$\Rightarrow 9x = 99$$

$$\Rightarrow x = 11.$$

$$\therefore$$ The smaller number $$= (3 \times 11) = 33.$$

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3.

The fourth proportional to $$5, 8, 15$$ is:

Let the fourth proportional to $$5, 8 , 15$$ be $$x.$$

Then, $$5 : 8 : 15 : x$$

$$\Rightarrow 5x = (8 \times 15)$$

$$x = \frac{(8 \times 15)}{5} = 24.$$

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4.

If $$40$$% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

Let $$40$$% of $$A = \frac{2}{3} B$$

Then, $$\frac{40A}{100} = \frac{2B}{3}$$

$$\Rightarrow \frac{2A}{5} = \frac{2B}{3}$$

$$\Rightarrow \frac{A}{B} = (\frac{2}{3} \times \frac{5}{2}) = \frac{5}{3}$$

$$\therefore A : B = 5 : 3.$$

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5.

The salaries $$A, B, C$$ are in the ratio $$2 : 3 : 5.$$ If the increments of $$15$$%, $$10$$% and $$20$$% are allowed respectively in their salaries, then what will be new ratio of their salaries?

Let $$A = 2k, B = 3k$$ and $$C = 5k.$$

$$A's$$ new salary $$= \frac{115}{100}$$ of $$2k = (\frac{115}{100} \times 2k) = \frac{23k}{10}$$

$$B's$$ new salary $$= \frac{110}{100}$$ of $$3k = (\frac{110}{100} \times 3k) = \frac{33k}{10}$$

$$C's$$ new salary $$= \frac{120}{100}$$ of $$5k = (\frac{120}{100} \times 5k) = 6k$$

$$\therefore$$ New ratio $$(\frac{23k}{10} : \frac{33k}{10} : 6k) = 23 : 33 : 60$$