Practice Questions for Arithmetic - Ratio, Proportion & Variation

1. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

The monthly incomes of A and B are in the ratio of 3 : 2 and their expenditures are in the ratio of 5 : 3. Each saves Rs. 1000 a month; find their incomes.

(a)
1000, 2000
(b)
2000, 4000
(c)
6000, 4000
(d)
None of these

2. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

A purse contains 144 coins comprising one rupee, 50 paise and 25 paise coins, their values being in the ratio 10 : 15 : 8. Find the number of 25 paise coins.

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7 8 9 4 5 6 1 2 3 0 . -

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3. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

In a class, 3/5^th of the students are girls and 1/3^rd of them travel to school by bus, 36 girls of that class do not travel to school by bus. Find the strength of the class.

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7 8 9 4 5 6 1 2 3 0 . -

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4. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

If $\frac{a}{b} = \frac{2}{1}$ and $\frac{p}{q} = \frac{3}{2}$ , then find $\frac{2 a p - b q}{3 a p + 2 b q}$ .

(a)
3/7
(b)
5/8
(c)
5/11
(d)
3/2

Answer: Option C

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Explanation :

Given that a/b = 2/1 and p/q = 3/2

a = 2b and p = 3/2 q

∴ $\frac{2 a p - b q}{3 a p + 2 b q}$ = $\frac{2 \times 2 b \times \frac{3}{2} q - b q}{3 \times 2 b \times \frac{3}{2} q + 2 b q}$ = $\frac{6 b q - b q}{9 b q + 2 b q} = \frac{5 b q}{11 b q}$ = $\frac{5}{11}$

Hence, option (c).

5. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

If X : Y = 4 : 3, find the ratio $\frac{(3 X^{2} - 2 Y^{2})}{(3 X^{2} + 2 Y^{2})}$ .

(a)
7 : 9
(b)
2 : 3
(c)
5 : 11
(d)
11 : 13

Answer: Option C

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Explanation :

X/Y = 4/3

⇒ X= 4Y/3

⇒ X²= (16Y²)/9

Then, $\frac{(3 \times \frac{16}{9} Y^{2} - 2 Y^{2})}{(3 \times \frac{16}{9} Y^{2} + 2 Y^{2})} = \frac{10 Y^{2}}{22 Y^{2}} = \frac{5}{11}$ or 5 : 11.

Hence, option (c).

6. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

The ratio of the present ages of Akanksha and Netra is 2 : 1. 8 years hence, Netra would be as old as Akanksha is now. Find the present ages (in years) of Netra and Akanksha respectively.

(a)
8, 16
(b)
16, 8
(c)
7, 3
(d)
3, 7

7. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

x + 2y – 3z = 0 and 2x – 3y – 5z = 0. Find x : y : z.

(a)
10 : 5 : 1
(b)
1 : 1 : 1
(c)
7 : 19 : 1
(d)
19 : 1 : 7

8. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

What must be added to both the terms x and y so that their ratio becomes equal to p : q?

(a)
$\frac{x q + y p}{p + q}$
(b)
$\frac{x p + y q}{p + q}$
(c)
$\frac{x q - y p}{p - q}$
(d)
$\frac{x p - y q}{p - q}$

9. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

Divide Rs. 375 among A, B and C so that if Rs. 4, Rs. 5, Rs. 6 be subtracted from their respective shares, the remainder may be in the ratio 3 : 4 : 5.

(a)
175, 125, 75
(b)
120, 125, 130
(c)
94, 125, 156
(d)
90, 125, 160

10. PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

For which of the following values of a : b is (4a² + 2ab) : (2ab + b²) = 5 : 1? a & b are natural numbers.

(a)
1 : 2
(b)
3 : 5
(c)
5 : 2
(d)
More than one of the above

Answer: Option C

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Explanation :

$\frac{4 a^{2} + 2 a b}{2 a b + b^{2}} = \frac{5}{1}$

⇒ $\frac{2 a (2 a + b)}{b (2 a + b)} = \frac{5}{1}$

⇒ 2a/b = 5/1

⇒ a/b = 5/2

Hence, option (c).

PE 1 - Ratio | Arithmetic - Ratio, Proportion & Variation

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