Practice Questions for Ratio, Proportion & Variation

1. CRE 1 - Ratio | Ratio, Proportion & Variation

Anand divided 70 sweets among his daughters Rohini and Sushma in the ratio 4 : 3. How many sweets did Rohini get?

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Answer: 40

Explanation :

Since, the ratio of sweets that Rohini and Sushma get is 4 : 3, let the number of sweets received by Rohini is 4x and Sushma is 3x.

According to question, 4x + 3x = 70

⇒ 7x = 70

⇒ x = 10

∴ Sweets received by Rohini = 4x = 4 × 10 = 40.

Alternately,

Number of sweets that Rohini got = $\frac{4}{4 + 3}$ × 70 = 40

Hence, 40.

2. CRE 1 - Ratio | Ratio, Proportion & Variation

If x : y = 4 : 3, find 5x : 7y.

(a)
15/28
(b)
3/4
(c)
20/21
(d)
20/37

Answer: Option C

Explanation :

$\frac{x}{y} = \frac{4}{3}$

$\frac{5 x}{7 y} = \frac{5}{7} (\frac{4}{3}) = \frac{20}{21}$

Hence, option (c).

3. CRE 1 - Ratio | Ratio, Proportion & Variation

Ratio of two numbers is 4 : 5 and their sum is 144. Find the smaller of the two numbers.

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4. CRE 1 - Ratio | Ratio, Proportion & Variation

The greatest ratio out of 2 : 3, 5 : 4, 3 : 2 and 4 : 5 is?

(a)
4 : 5
(b)
3 : 2
(c)
5 : 4
(d)
2 : 3

Answer: Option B

Explanation :

Here, only 5/4 and 3/2 are greater than 1. So, let’s consider only these two ratios. Other 2 ratios are smaller than 1.

To find the greatest ratio, we must bring each of the ratio to common denominator.

Thus, $\frac{5}{4}, \frac{3}{2}$ ≡ $\frac{5}{4}, \frac{3}{2} \times \frac{2}{2}$ ≡ $\frac{5}{4}, \frac{6}{4}$

Hence, ratio 3 : 2 is the greatest ratio.

Hence, option (b).

Alternately,

If a/b > 1, ⇒ $\frac{a + x}{b + x} < \frac{a}{b}$

Hence, $\frac{5}{4}$ = $\frac{3 + 2}{2 + 2}$ < $\frac{3}{2}$ .

Alternately,

Assume $\frac{5}{4} > \frac{3}{2}$

⇒ 5 × 2 > 3 × 4

⇒ 10 > 12, which is not true.

Hence our assumption was wrong.

∴ 3/2 is the greatest ratio.

Hence, option (b).

5. CRE 1 - Ratio | Ratio, Proportion & Variation

The smallest ratio out of 1 : 2, 2 : 1, 1 : 3 and 3 : 1 is?

(a)
3 : 1
(b)
1 : 3
(c)
2 : 1
(d)
1 : 2

6. CRE 1 - Ratio | Ratio, Proportion & Variation

The ratio of two numbers is 3 : 5 and their sum is 72. Find the larger of the two numbers.

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7. CRE 1 - Ratio | Ratio, Proportion & Variation

The present ages of two persons are in the ratio 15 : 17. Twenty-four years ago the ratio of their ages was 9 : 11. Find the present age of the older person.

(a)
64 years
(b)
72 years
(c)
56 years
(d)
68 years

Answer: Option D

Explanation :

Let their present ages be 15x and 17x years respectively.

Ratio of their ages 24 years ago:

$\frac{15 x - 24}{17 x - 24} = \frac{9}{11}$

⇒ 165x – 264 = 153x - 216

⇒ 12x = 48

⇒ x = 4

∴ The age of the older person is 17 × 4 i.e., 68 years

Hence, option (d).

8. CRE 1 - Ratio | Ratio, Proportion & Variation

The ratio of the number of students in 3 sections A, B and C is 3 : 7 : 8. If there are a total of 360 students in these sections, find the number of students in section A.

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Answer: 60

Explanation :

Let the number of students in A, B and C be 3x, 7x and 8x respectively.

3x + 7x + 8x = 360

⇒ x = 20

⇒ 3x = 60

Hence, 60.

Alternately,

Number of students in section A = $\frac{3}{3 + 7 + 8}$ × 360 = 60

Hence, 60.

9. CRE 1 - Ratio | Ratio, Proportion & Variation

The present ages of Anand and Ashish are in the ratio 4 : 5. 10 years hence, the ratio of their ages will be 5 : 6. Find the present age of Anand. (in years)

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Answer: 40

Explanation :

Let the present ages of Anand and Ashish be 4x years and 5x years respectively.

The ratio of their ages 10 years hence = $\frac{4 x + 10}{5 x + 10} = \frac{5}{6}$

⇒ 24x + 60 = 25x + 50

⇒ 10 = x

Therefore, Anand’s present age is 4 × 10 = 40 years.

Hence, 40.

10. CRE 1 - Ratio | Ratio, Proportion & Variation

Find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second numbers added to the difference of the third and the second numbers is 42.

(a)
24, 16, 32
(b)
12, 8, 16
(c)
18, 12, 48
(d)
18, 12, 24

11. CRE 1 - Ratio | Ratio, Proportion & Variation

156 is divided into two parts such that seven times the first part and five times the second part are in the ratio 5 : 2. Find the first part.

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Answer: 100

Explanation :

Let the numbers be x and 156 – x

$\frac{7 x}{5 (156 - x)} = \frac{5}{2}$

⇒ 14x = 25 × 156 - 25x

⇒ 39x = 25 × 156

⇒ x = 25 × 4 = 100

∴ The first part is 100.

Hence, 100.

Alternately,

Let the numbers be a and b.

Hence, a + b = 156, and

$\frac{7 a}{5 b} = \frac{5}{2}$

⇒ $\frac{a}{b} = \frac{25}{14}$

⇒ a = 25/39 × 156 = 100.

Hence, 100.

12. CRE 1 - Ratio | Ratio, Proportion & Variation

If a : b = 3 : 7, find the value of (4a + b) : (3a + 5b).

(a)
12 : 41
(b)
19 : 32
(c)
12 : 47
(d)
19 : 44

Answer: Option D

Explanation :

Let a = 3k, b = 7k

∴ $\frac{4 a + b}{3 a + 5 b} = \frac{4 \times 3 k + 7 k}{3 \times 3 k + 5 \times 7 k}$ = $\frac{19 k}{44 k} = \frac{19}{44}$

Hence, option (d).

Alternately,

We have to find the value of $\frac{4 a + b}{3 a + 5 b}$

Dividing both numerator and denominator with b, we get

$\frac{4 (\frac{a}{b}) + 1}{3 (\frac{a}{b}) + 5} = \frac{4 (\frac{3}{7}) + 1}{3 (\frac{3}{7}) + 5}$ = $\frac{12 + 7}{9 + 35} = \frac{19}{44}$

Hence, option (d).

13. CRE 1 - Ratio | Ratio, Proportion & Variation

In a group of 60 students, which of the following can’t be the ratio of males and females?

(a)
2 : 3
(b)
1 : 5
(c)
2 : 7
(d)
2 : 1

Answer: Option C

Explanation :

Let the ratio of males and females be m : f.

We know the number of males will be $\frac{m}{m + f} \times 60$

Consider option (c), m = 2 and f = 7. This cannot be the ratio because 60 is not divisible by (2 + 7) i.e. 9.

Hence, option (c).

14. CRE 1 - Ratio | Ratio, Proportion & Variation

If a : b = 3 : 2 and b : c = 7 : 5, then find a : b : c.

(a)
10 : 15 : 21
(b)
21 : 14 : 10
(c)
9 : 12 : 14
(d)
12 : 7 : 18

15. CRE 1 - Ratio | Ratio, Proportion & Variation

If A is 1/3^rd of B and B is 1/2 of C, then A : B : C is?

(a)
1 : 3 :6
(b)
2 : 3 : 6
(c)
3 : 2 : 6
(d)
None of these

Answer: Option A

Explanation :

A = B/3, B = C/2, C = C, then,

A : B : C = $\frac{B}{3} : \frac{C}{2} : \frac{C}{1} = \frac{C}{3 \times 2} : \frac{C}{2} : \frac{C}{1}$ = $\frac{1}{6} : \frac{1}{2} : \frac{1}{1}$ = $\frac{6}{6} : \frac{6}{2} : \frac{6}{1}$ = 1 : 3 : 6

Hence, option (a).

16. CRE 1 - Ratio | Ratio, Proportion & Variation

If A : B = 3 : 2, B : C = 4 : 3, C : D = 5 : 4, then A : D is?

(a)
5 : 2
(b)
30 : 20
(c)
15 : 12
(d)
None of these

17. CRE 1 - Ratio | Ratio, Proportion & Variation

The ratio of two numbers is 3 : 2 and their difference is 225, the smaller number is:

(a)
90
(b)
675
(c)
135
(d)
450

18. CRE 1 - Ratio | Ratio, Proportion & Variation

What should be subtracted from the numbers in the ratio 9 : 16 so as to get 1 : 2?

(a)
8
(b)
14
(c)
2
(d)
Cannot be determined

Answer: Option D

Explanation :

Two numbers are in the ratio of 9 : 16. Let the numbers be 9x and 16x.

Now, let a be subtracted to get new ratio as 1 : 2.

∴ $\frac{9 x - a}{16 x - a} = \frac{1}{2}$

⇒ 18x - 2a = 16x - a

⇒ 2x = a

Since we do not know the value of x, we cannot find out the value of a.

Hence, option (d).

19. CRE 1 - Ratio | Ratio, Proportion & Variation

If A : B = 2 : 3, B : C = 3 : 4 and C : D = 4 : 5, then, A : B : C : D is?

(a)
2 : 3 : 4 : 5
(b)
5 : 2 : 3 : 7
(c)
3 : 4 : 7 : 8
(d)
None of these

20. CRE 1 - Ratio | Ratio, Proportion & Variation

If $\frac{p + q}{2 p + q} = \frac{3}{4}$ , then find $\frac{3 p + q}{2 p + q}$ .

(a)
4/5
(b)
5/4
(c)
6/7
(d)
3/4

Answer: Option B

Explanation :

Given that, $\frac{p + q}{2 p + q} = \frac{3}{4}$

⇒ 4(p + q) = 3(2p + q)

⇒ 4p + 4q = 6p + 3q ⇒ q = 2p

Now, $\frac{3 p + q}{2 p + q} = \frac{3 p + 2 p}{2 p + 2 p} = \frac{5 p}{4 p} = \frac{5}{4}$

Hence, option (b).

21. CRE 1 - Ratio | Ratio, Proportion & Variation

If p + q + r = 180 and p = q/2 and q = r/3, find r.

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Answer: 120

Explanation :

p = $\frac{q}{2}$ ⇒ $\frac{p}{q} = \frac{1}{2}$

q = $\frac{r}{3}$ ⇒ $\frac{q}{r} = \frac{1}{3} = \frac{2}{6}$

So, p : q : r = 1 : 2 : 6

So, r = $\frac{6}{1 + 2 + 3}$ × 180 = 120.

Hence, 120.

22. CRE 1 - Ratio | Ratio, Proportion & Variation

If p : q = 3 : 1, find $\frac{p - 2 q}{3 p - q^{2}}$ .

(a)
2/7
(b)
1/8
(c)
3/7
(d)
Cannot be determined

Answer: Option D

Explanation :

Given that p : q = 3 : 1

p/q = 3/1

p = 3q

$\frac{p - 2 q}{3 p - q^{2}} = \frac{3 q - 2 q}{3 (3 q) - q^{2}}$ (∵ p = 3q)

= $\frac{q}{9 q - q^{2}} = \frac{1}{9 - q}$

Since we don’t know the value of ‘q’, the answer cannot be determined.

Hence, option (d).

23. CRE 1 - Ratio | Ratio, Proportion & Variation

At a party, there are a total of 56 people. If ‘m’ men join the party, the ratio of the number of ladies to that of men will change from 4 : 3 to 4 : 5. Find m.

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Answer: 16

Explanation :

Number of ladies at the party do not change.

Initial number of ladies = (4/7) × 56 = 32.

Initial number of men = 56 - 32 - 24.

After x men join,

$\frac{l a d i e s}{m e n} = \frac{4}{5}$

the number of men would be 5/4 × (Number of ladies) = 5/4 × 32 = 40

∴ the number of men joining (m) = 40 – 24 = 16.

Hence, 16.

24. CRE 1 - Ratio | Ratio, Proportion & Variation

Rs. 1500 is divided among, A, B and C such that A receives 1/3^rd as much as B and C together. A’s share is?

(a)
Rs. 600
(b)
Rs. 525
(c)
Rs. 375
(d)
Rs. 0

25. CRE 1 - Ratio | Ratio, Proportion & Variation

The monthly salaries of A and B are in the ratio 2 : 3. The monthly expenditures of X and Y are in the ratio 3 : 4. Find the ratio of the monthly savings of X and Y.

(a)
5 : 3
(b)
3 : 5
(c)
4 : 7
(d)
Cannot be determined

Answer: Option D

Explanation :

Let the monthly salaries of A and B be Rs. 2x and Rs. 3x respectively.

Let the monthly expenditures of A and B be Rs. 3y and Rs. 4y respectively.

Ratio of the monthly savings of A and B = $\frac{2 x - 3 y}{3 x - 4 y} = \frac{2 (\frac{x}{y}) - 3}{3 (\frac{x}{y}) - 4}$ .

As x/y is unknown, the ratio cannot be found

Hence, option (d).

CRE 1 - Ratio | Ratio, Proportion & Variation

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