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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?

Answer: C

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:

Answer: B

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:

Answer: D

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?

Answer: C

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?

Answer: C

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 \((\frac{23k}{10} : \frac{33k}{10} : 6k) = 23 : 33 : 60\)

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