Ratio and Proportion — Practice Questions – KLEE Arithmetic & Mental Ability Test 2
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Solved examples
A school has 2140 students, of whom 1200 are girls. The ratio of boys to girls is:
Answer: 47 : 60 — Boys = 940; 940 : 1200 = 47 : 60.
What is the ratio of ₹2.80 to 40 paise?
Answer: 7 : 1 — 280 paise : 40 paise = 7 : 1.
The ratio of a number to the number obtained by adding one-fifth of it to itself is:
Answer: 5 : 6 — x : 6x/5 = 5 : 6.
If 60% of A = 3/4 of B, then A : B is:
Answer: 5 : 4 — (3/5)A = (3/4)B → A/B = 5/4.
If (2/3)A = 75% of B, then A : B is:
Answer: 9 : 8 — A/B = (3/4) × (3/2) = 9/8.
A jar has 10 black and white marbles. Which could NOT be the ratio of black to white?
Answer: 1 : 10 — The sum of the ratio terms must divide 10; 1 + 10 = 11 does not.
Boys : girls in a club = 3 : 2. Which could be the actual number of members? (16, 18, 24, 25)
Answer: 25 — The total must be a multiple of 5.
Which of the following is the lowest ratio? (7 : 15, 15 : 23, 17 : 25, 21 : 39)
Answer: 7 : 15 — 7/15 = 0.466 is the smallest.
If 5 : a :: 20 : 28, then a = ?
Answer: 7 — 20a = 5 × 28 = 140 → a = 7.
If 3/4 : 1/2 :: 27y : ?, the missing term is:
Answer: 18y — ? = (1/2)(27y) ÷ (3/4) = 18y.
If x : 7.5 = 7 : 17.5, then x = ?
Answer: 3 — x = 7.5 × 7/17.5 = 3.
The simplest form of the ratio 3 hours : 1 day is:
Answer: 1 : 8 — 3 : 24 = 1 : 8.
The simplest form of the ratio 1.5 : 2.5 is:
Answer: 3 : 5 — 15 : 25 = 3 : 5.
Practice questions
A school has 1,800 students, of whom 1,050 are girls. The ratio of boys to girls is:
- A. 5 : 12
- B. 7 : 5
- C. 3 : 4
- D. 5 : 7
Answer: Option D
Explanation:
Boys = 750; 750 : 1050 = 5 : 7.
A school has 960 students, of whom 540 are boys. The ratio of boys to girls is:
- A. 4 : 3
- B. 9 : 7
- C. 7 : 9
- D. 9 : 16
Answer: Option B
Explanation:
Girls = 420; 540 : 420 = 9 : 7.
A school has 2,500 students, of whom 1,100 are girls. The ratio of boys to girls is:
- A. 7 : 5
- B. 11 : 25
- C. 11 : 14
- D. 14 : 11
Answer: Option D
Explanation:
Boys = 1400; 1400 : 1100 = 14 : 11.
A class of 45 has 18 girls. The ratio of boys to the total number of students is:
- A. 2 : 3
- B. 2 : 5
- C. 3 : 2
- D. 3 : 5
Answer: Option D
Explanation:
Boys = 27; 27 : 45 = 3 : 5.
A school has 3,600 students, of whom 1,600 are boys. The ratio of girls to boys is:
- A. 5 : 4
- B. 4 : 5
- C. 5 : 9
- D. 4 : 9
Answer: Option A
Explanation:
Girls = 2000; 2000 : 1600 = 5 : 4.
What is the ratio of ₹1.20 to 30 paise?
- A. 4 : 1
- B. 1 : 4
- C. 2 : 5
- D. 40 : 1
Answer: Option A
Explanation:
120 paise : 30 paise = 4 : 1.
What is the ratio of 75 paise to ₹3?
- A. 1 : 4
- B. 25 : 1
- C. 4 : 1
- D. 1 : 25
Answer: Option A
Explanation:
75 paise : 300 paise = 1 : 4.
What is the ratio of ₹4.50 to 90 paise?
- A. 2 : 1
- B. 5 : 1
- C. 1 : 20
- D. 1 : 5
Answer: Option B
Explanation:
450 paise : 90 paise = 5 : 1.
What is the ratio of 2 km to 400 m?
- A. 1 : 5
- B. 200 : 1
- C. 5 : 1
- D. 1 : 200
Answer: Option C
Explanation:
2000 m : 400 m = 5 : 1.
What is the ratio of 45 minutes to 2 hours?
- A. 3 : 4
- B. 45 : 2
- C. 8 : 3
- D. 3 : 8
Answer: Option D
Explanation:
45 min : 120 min = 3 : 8.
The ratio of a number to the number obtained by adding one-third of it to itself is:
- A. 4 : 3
- B. 1 : 3
- C. 3 : 4
- D. 3 : 1
Answer: Option C
Explanation:
x : 4x/3 = 3 : 4.
The ratio of a number to the number obtained by subtracting one-fourth of it from itself is:
- A. 3 : 4
- B. 4 : 5
- C. 4 : 3
- D. 1 : 4
Answer: Option C
Explanation:
x : 3x/4 = 4 : 3.
The ratio of a number increased by two-fifths of itself to the number is:
- A. 3 : 5
- B. 5 : 7
- C. 7 : 5
- D. 2 : 5
Answer: Option C
Explanation:
7x/5 : x = 7 : 5.
The ratio of a number to the number obtained by adding three-sevenths of it to itself is:
- A. 10 : 7
- B. 7 : 10
- C. 7 : 3
- D. 3 : 7
Answer: Option B
Explanation:
x : 10x/7 = 7 : 10.
The ratio of a number decreased by one-sixth of itself to the number is:
- A. 6 : 5
- B. 7 : 6
- C. 1 : 6
- D. 5 : 6
Answer: Option D
Explanation:
5x/6 : x = 5 : 6.
If 80% of A = 2/5 of B, then A : B is:
- A. 2 : 5
- B. 4 : 5
- C. 1 : 2
- D. 2 : 1
Answer: Option C
Explanation:
(4/5)A = (2/5)B → A/B = 1/2.
If 45% of A = 3/5 of B, then A : B is:
- A. 9 : 10
- B. 4 : 3
- C. 3 : 4
- D. 3 : 5
Answer: Option B
Explanation:
(9/20)A = (3/5)B → A/B = (3/5)/(9/20) = 4/3.
If 35% of A = 7/10 of B, then A : B is:
- A. 1 : 2
- B. 7 : 10
- C. 2 : 1
- D. 7 : 2
Answer: Option C
Explanation:
(7/20)A = (7/10)B → A/B = 2.
If 90% of A = 3/4 of B, then A : B is:
- A. 6 : 5
- B. 3 : 4
- C. 9 : 10
- D. 5 : 6
Answer: Option D
Explanation:
(9/10)A = (3/4)B → A/B = (3/4)/(9/10) = 5/6.
If 15% of A = 1/4 of B, then A : B is:
- A. 3 : 5
- B. 3 : 20
- C. 4 : 15
- D. 5 : 3
Answer: Option D
Explanation:
(3/20)A = (1/4)B → A/B = (1/4)/(3/20) = 5/3.
If (3/5)A = 40% of B, then A : B is:
- A. 4 : 5
- B. 2 : 3
- C. 3 : 5
- D. 3 : 2
Answer: Option B
Explanation:
(3/5)A = (2/5)B → A/B = 2/3.
If (3/4)A = 60% of B, then A : B is:
- A. 4 : 5
- B. 9 : 20
- C. 3 : 4
- D. 5 : 4
Answer: Option A
Explanation:
(3/4)A = (3/5)B → A/B = (3/5)/(3/4) = 4/5.
If (5/6)A = 50% of B, then A : B is:
- A. 3 : 5
- B. 5 : 6
- C. 6 : 5
- D. 5 : 3
Answer: Option A
Explanation:
(5/6)A = (1/2)B → A/B = (1/2)/(5/6) = 3/5.
If (1/2)A = 80% of B, then A : B is:
- A. 5 : 2
- B. 8 : 5
- C. 2 : 5
- D. 5 : 8
Answer: Option B
Explanation:
(1/2)A = (4/5)B → A/B = 8/5.
If (4/7)A = 20% of B, then A : B is:
- A. 7 : 20
- B. 4 : 35
- C. 20 : 7
- D. 5 : 7
Answer: Option A
Explanation:
(4/7)A = (1/5)B → A/B = (1/5)/(4/7) = 7/20.
A jar has 12 black and white marbles. Which could NOT be the ratio of black to white?
- A. 2 : 3
- B. 5 : 7
- C. 1 : 3
- D. 1 : 2
Answer: Option A
Explanation:
2 + 3 = 5 does not divide 12; 3, 12 and 4 do.
A jar has 15 black and white marbles. Which could NOT be the ratio of black to white?
- A. 2 : 3
- B. 1 : 4
- C. 7 : 8
- D. 3 : 4
Answer: Option D
Explanation:
3 + 4 = 7 does not divide 15; 5, 5 and 15 do.
A jar has 20 black and white marbles. Which could NOT be the ratio of black to white?
- A. 3 : 7
- B. 1 : 3
- C. 2 : 5
- D. 9 : 11
Answer: Option C
Explanation:
2 + 5 = 7 does not divide 20; 4, 10 and 20 do.
A jar has 18 black and white marbles. Which could NOT be the ratio of black to white?
- A. 7 : 11
- B. 1 : 2
- C. 3 : 5
- D. 4 : 5
Answer: Option C
Explanation:
3 + 5 = 8 does not divide 18; 3, 9 and 18 do.
A jar has 30 black and white marbles. Which could NOT be the ratio of black to white?
- A. 2 : 3
- B. 3 : 4
- C. 1 : 5
- D. 7 : 8
Answer: Option B
Explanation:
3 + 4 = 7 does not divide 30; 5, 15 and 6 do.
Boys : girls in a club = 4 : 3. Which could be the total number of members?
- A. 40
- B. 45
- C. 50
- D. 49
Answer: Option D
Explanation:
The total must be a multiple of 4 + 3 = 7; only 49 is.
Boys : girls in a club = 5 : 4. Which could be the total number of members?
- A. 56
- B. 60
- C. 54
- D. 50
Answer: Option C
Explanation:
The total must be a multiple of 9; only 54 is.
Boys : girls in a club = 2 : 5. Which could be the total number of members?
- A. 50
- B. 63
- C. 65
- D. 60
Answer: Option B
Explanation:
The total must be a multiple of 7; only 63 is.
Boys : girls in a club = 7 : 3. Which could be the total number of members?
- A. 80
- B. 84
- C. 63
- D. 75
Answer: Option A
Explanation:
The total must be a multiple of 10; only 80 is.
Boys : girls in a club = 3 : 8. Which could be the total number of members?
- A. 80
- B. 88
- C. 90
- D. 96
Answer: Option B
Explanation:
The total must be a multiple of 11; only 88 is.
Which of the following is the greatest ratio?
- A. 3 : 4
- B. 11 : 15
- C. 7 : 9
- D. 5 : 6
Answer: Option D
Explanation:
5/6 = 0.833, 7/9 = 0.778, 11/15 = 0.733, 3/4 = 0.75.
Which of the following is the lowest ratio?
- A. 5 : 9
- B. 4 : 7
- C. 2 : 3
- D. 3 : 5
Answer: Option A
Explanation:
2/3 = 0.667, 3/5 = 0.6, 4/7 = 0.571, 5/9 = 0.556.
Which of the following is the greatest ratio?
- A. 13 : 20
- B. 2 : 3
- C. 7 : 11
- D. 8 : 13
Answer: Option B
Explanation:
13/20 = 0.65, 8/13 = 0.615, 2/3 = 0.667, 7/11 = 0.636.
Which of the following is the lowest ratio?
- A. 5 : 11
- B. 4 : 9
- C. 7 : 16
- D. 9 : 20
Answer: Option C
Explanation:
9/20 = 0.45, 4/9 = 0.444, 5/11 = 0.4545, 7/16 = 0.4375.
Which of the following is the greatest ratio?
- A. 9 : 10
- B. 17 : 19
- C. 8 : 9
- D. 13 : 15
Answer: Option A
Explanation:
17/19 = 0.895, 13/15 = 0.867, 8/9 = 0.889, 9/10 = 0.9.
If 6 : a :: 18 : 33, then a = ?
- A. 12
- B. 9
- C. 11
- D. 99
Answer: Option C
Explanation:
18a = 6 × 33 = 198 → a = 11.
If 4 : 9 :: 12 : a, then a = ?
- A. 36
- B. 18
- C. 27
- D. 24
Answer: Option C
Explanation:
4a = 9 × 12 = 108 → a = 27.
If a : 12 :: 15 : 36, then a = ?
- A. 45
- B. 5
- C. 4
- D. 6
Answer: Option B
Explanation:
36a = 12 × 15 = 180 → a = 5.
If 8 : 14 :: a : 35, then a = ?
- A. 24
- B. 28
- C. 16
- D. 20
Answer: Option D
Explanation:
14a = 8 × 35 = 280 → a = 20.
If 7 : a :: 21 : 39, then a = ?
- A. 13
- B. 117
- C. 12
- D. 14
Answer: Option A
Explanation:
21a = 7 × 39 = 273 → a = 13.
If 2/3 : 1/2 :: 16y : ?, the missing term is:
- A. 24y
- B. 8y
- C. 12y
- D. 18y
Answer: Option C
Explanation:
? = (1/2)(16y) ÷ (2/3) = 8y × 3/2 = 12y.
If 5/6 : 1/3 :: 25y : ?, the missing term is:
- A. 10y
- B. 5y
- C. 15y
- D. 50y
Answer: Option A
Explanation:
? = (1/3)(25y) ÷ (5/6) = (25/3)y × 6/5 = 10y.
If 1/2 : 3/4 :: 10y : ?, the missing term is:
- A. 20y
- B. 15y
- C. 12y
- D. 7.5y
Answer: Option B
Explanation:
? = (3/4)(10y) ÷ (1/2) = 15y.
If 4/5 : 2/5 :: 18y : ?, the missing term is:
- A. 9y
- B. 12y
- C. 36y
- D. 6y
Answer: Option A
Explanation:
? = (2/5)(18y) ÷ (4/5) = 9y.
If 3/8 : 1/4 :: 12y : ?, the missing term is:
- A. 8y
- B. 9y
- C. 18y
- D. 6y
Answer: Option A
Explanation:
? = (1/4)(12y) ÷ (3/8) = 3y × 8/3 = 8y.
If x : 4.5 = 8 : 6, then x = ?
- A. 6
- B. 3.375
- C. 5
- D. 4
Answer: Option A
Explanation:
x = 4.5 × 8/6 = 6.
If x : 2.5 = 12 : 7.5, then x = ?
- A. 3
- B. 36
- C. 4
- D. 5
Answer: Option C
Explanation:
x = 2.5 × 12/7.5 = 4.
If 3.6 : x = 9 : 12.5, then x = ?
- A. 5
- B. 6
- C. 4.5
- D. 4
Answer: Option A
Explanation:
9x = 3.6 × 12.5 = 45 → x = 5.
If x : 0.8 = 15 : 6, then x = ?
- A. 0.32
- B. 2
- C. 1.5
- D. 2.5
Answer: Option B
Explanation:
x = 0.8 × 15/6 = 2.
If 1.4 : 3.5 = x : 20, then x = ?
- A. 7
- B. 10
- C. 50
- D. 8
Answer: Option D
Explanation:
3.5x = 1.4 × 20 = 28 → x = 8.
The simplest form of 45 minutes : 1 hour is:
- A. 3 : 5
- B. 3 : 4
- C. 45 : 1
- D. 4 : 3
Answer: Option B
Explanation:
45 : 60 = 3 : 4.
The simplest form of 20 minutes : 2 hours is:
- A. 1 : 12
- B. 10 : 1
- C. 1 : 10
- D. 1 : 6
Answer: Option D
Explanation:
20 : 120 = 1 : 6.
The simplest form of 6 months : 2 years is:
- A. 3 : 1
- B. 1 : 2
- C. 1 : 3
- D. 1 : 4
Answer: Option D
Explanation:
6 : 24 = 1 : 4.
The simplest form of 250 g : 2 kg is:
- A. 1 : 8
- B. 125 : 1
- C. 1 : 4
- D. 8 : 1
Answer: Option A
Explanation:
250 : 2000 = 1 : 8.
The simplest form of 40 cm : 2 m is:
- A. 1 : 50
- B. 20 : 1
- C. 1 : 5
- D. 2 : 5
Answer: Option C
Explanation:
40 : 200 = 1 : 5.
The simplest form of 0.4 : 1.2 is:
- A. 3 : 1
- B. 1 : 3
- C. 2 : 3
- D. 4 : 12
Answer: Option B
Explanation:
4 : 12 = 1 : 3.
The simplest form of 2.25 : 1.5 is:
- A. 2 : 3
- B. 15 : 10
- C. 3 : 2
- D. 9 : 4
Answer: Option C
Explanation:
225 : 150 = 3 : 2.
The simplest form of 0.36 : 0.48 is:
- A. 9 : 16
- B. 4 : 3
- C. 36 : 48
- D. 3 : 4
Answer: Option D
Explanation:
36 : 48 = 3 : 4.
The simplest form of 1.6 : 2.4 is:
- A. 8 : 15
- B. 2 : 3
- C. 3 : 2
- D. 4 : 6
Answer: Option B
Explanation:
16 : 24 = 2 : 3.
The simplest form of 4.5 : 0.9 is:
- A. 45 : 9
- B. 5 : 1
- C. 1 : 5
- D. 9 : 2
Answer: Option B
Explanation:
45 : 9 = 5 : 1.