Ratio and Proportion — Full Practice Set – KLEE Arithmetic & Mental Ability Test 1
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Solved examples
A and B together have Rs. 1210. If 4/15 of A's amount equals 2/5 of B's amount, how much does B have?
Answer: Rs. 484 — A : B = 3 : 2, so B = 1210 × 2/5 = 484.
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Answer: 4 : 5 — 120 : 150 = 4 : 5.
Money is divided among A, B, C, D in the proportion 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Answer: Rs. 2000 — 4x − 3x = 1000 → x = 1000; B = 2x = 2000.
Seats for Mathematics, Physics and Biology are in the ratio 5 : 7 : 8. They are increased by 40%, 50% and 75%. The new ratio is:
Answer: 2 : 3 : 4 — 7x : 21x/2 : 14x = 14 : 21 : 28 = 2 : 3 : 4.
Boys : girls in a college = 7 : 8. If boys increase by 20% and girls by 10%, the new ratio is:
Answer: 21 : 22 — 42x/5 : 44x/5 = 21 : 22.
Salaries of Ravi and Sumit are 2 : 3. If each increases by Rs. 4000, the ratio becomes 40 : 57. What is Sumit's (new) salary?
Answer: Rs. 38,000 — 57(2x + 4000) = 40(3x + 4000) → 6x = 68000 → 3x = 34000; new = 38,000.
If 0.75 : x :: 5 : 8, then x = ?
Answer: 1.2 — 5x = 0.75 × 8 = 6 → x = 1.2.
The sum of three numbers is 98. First : second = 2 : 3 and second : third = 5 : 8. The second number is:
Answer: 30 — A : B : C = 10 : 15 : 24; B = 98 × 15/49 = 30.
If Rs. 782 is divided into three parts proportional to 1/2 : 2/3 : 3/4, the first part is:
Answer: Rs. 204 — Ratio = 6 : 8 : 9; first = 782 × 6/23 = 204.
Salaries of A, B, C are 2 : 3 : 5. After increments of 15%, 10% and 20%, the new ratio is:
Answer: 23 : 33 : 60 — 2.3 : 3.3 : 6 = 23 : 33 : 60.
If 40% of a number equals two-thirds of another, the ratio of the first to the second is:
Answer: 5 : 3 — (2/5)A = (2/3)B → A/B = 5/3.
The fourth proportional to 5, 8, 15 is:
Answer: 24 — 5 : 8 :: 15 : x → 5x = 120 → x = 24.
Two numbers are 3 : 5. If 9 is subtracted from each, they become 12 : 23. The smaller number is:
Answer: 33 — 23(3x − 9) = 12(5x − 9) → 9x = 99 → x = 11; smaller = 33.
Practice questions
A and B together have ₹1,500. If 1/3 of A's amount equals 1/2 of B's amount, how much does B have?
- A. ₹600
- B. ₹750
- C. ₹500
- D. ₹900
Answer: Option A
Explanation:
A/3 = B/2 → A : B = 3 : 2; B = 1500 × 2/5 = 600.
A and B together have ₹1,700. If 3/4 of A's amount equals 2/3 of B's amount, how much does B have?
- A. ₹900
- B. ₹850
- C. ₹1,000
- D. ₹800
Answer: Option A
Explanation:
(3/4)A = (2/3)B → A : B = 8 : 9; B = 1700 × 9/17 = 900.
A and B together have ₹1,800. If 1/4 of A's amount equals 1/5 of B's amount, how much does A have?
- A. ₹1,000
- B. ₹720
- C. ₹900
- D. ₹800
Answer: Option D
Explanation:
A/4 = B/5 → A : B = 4 : 5; A = 1800 × 4/9 = 800.
A and B together have ₹3,400. If 2/3 of A's amount equals 3/4 of B's amount, how much does A have?
- A. ₹1,800
- B. ₹1,700
- C. ₹1,600
- D. ₹2,000
Answer: Option A
Explanation:
(2/3)A = (3/4)B → A : B = 9 : 8; A = 3400 × 9/17 = 1800.
A and B together have ₹990. If 2/5 of A's amount equals 1/3 of B's amount, how much does B have?
- A. ₹450
- B. ₹540
- C. ₹600
- D. ₹495
Answer: Option B
Explanation:
(2/5)A = (1/3)B → A : B = 5 : 6; B = 990 × 6/11 = 540.
Two numbers are respectively 25% and 50% more than a third number. Their ratio is:
- A. 2 : 3
- B. 5 : 6
- C. 6 : 5
- D. 1 : 2
Answer: Option B
Explanation:
125 : 150 = 5 : 6.
Two numbers are respectively 10% and 40% more than a third number. Their ratio is:
- A. 1 : 4
- B. 11 : 12
- C. 11 : 14
- D. 7 : 11
Answer: Option C
Explanation:
110 : 140 = 11 : 14.
Two numbers are 20% less and 20% more than a third number respectively. Their ratio is:
- A. 3 : 4
- B. 2 : 3
- C. 1 : 1
- D. 4 : 5
Answer: Option B
Explanation:
80 : 120 = 2 : 3.
Two numbers are respectively 30% and 60% more than a third number. Their ratio is:
- A. 16 : 13
- B. 3 : 6
- C. 13 : 16
- D. 1 : 2
Answer: Option C
Explanation:
130 : 160 = 13 : 16.
Two numbers are 25% less and 50% more than a third number respectively. Their ratio is:
- A. 2 : 3
- B. 1 : 3
- C. 3 : 4
- D. 1 : 2
Answer: Option D
Explanation:
75 : 150 = 1 : 2.
Money is divided among A, B, C, D in the ratio 4 : 3 : 6 : 2. If C gets ₹1,200 more than A, what is B's share?
- A. ₹2,400
- B. ₹1,200
- C. ₹1,800
- D. ₹600
Answer: Option C
Explanation:
6x − 4x = 2x = 1200 → x = 600; B = 3x = 1800.
Money is divided among A, B, C, D in the ratio 2 : 3 : 5 : 4. If D gets ₹500 more than B, what is C's share?
- A. ₹2,000
- B. ₹1,500
- C. ₹2,500
- D. ₹3,000
Answer: Option C
Explanation:
4x − 3x = x = 500; C = 5x = 2500.
Money is divided among A, B, C, D in the ratio 6 : 4 : 3 : 7. If D gets ₹600 more than C, what is A's share?
- A. ₹750
- B. ₹1,050
- C. ₹900
- D. ₹600
Answer: Option C
Explanation:
7x − 3x = 4x = 600 → x = 150; A = 6x = 900.
Money is divided among A, B, C, D in the ratio 1 : 3 : 5 : 2. If C gets ₹2,400 more than B, what is the total sum?
- A. ₹6,000
- B. ₹12,000
- C. ₹14,400
- D. ₹13,200
Answer: Option D
Explanation:
5x − 3x = 2x = 2400 → x = 1200; total = 11x = 13,200.
Money is divided among A, B, C, D in the ratio 7 : 5 : 3 : 1. If A gets ₹1,800 more than B, what is D's share?
- A. ₹900
- B. ₹600
- C. ₹450
- D. ₹1,800
Answer: Option A
Explanation:
7x − 5x = 2x = 1800 → x = 900; D = x = 900.
Seats in three courses are in the ratio 4 : 5 : 6 and are increased by 25%, 20% and 50% respectively. The new ratio is:
- A. 5 : 6 : 9
- B. 4 : 5 : 6
- C. 5 : 6 : 8
- D. 6 : 5 : 9
Answer: Option A
Explanation:
4 × 1.25 = 5, 5 × 1.2 = 6, 6 × 1.5 = 9.
Seats in three courses are in the ratio 3 : 4 : 5 and are increased by 20%, 50% and 20% respectively. The new ratio is:
- A. 3 : 5 : 5
- B. 6 : 5 : 6
- C. 2 : 3 : 3
- D. 3 : 4 : 5
Answer: Option A
Explanation:
3.6 : 6 : 6 = 36 : 60 : 60 = 3 : 5 : 5.
Seats in three courses are in the ratio 2 : 3 : 5 and are increased by 50%, 100% and 20% respectively. The new ratio is:
- A. 1 : 3 : 2
- B. 1 : 2 : 2
- C. 3 : 6 : 5
- D. 2 : 3 : 3
Answer: Option B
Explanation:
2 × 1.5 = 3, 3 × 2 = 6, 5 × 1.2 = 6 → 3 : 6 : 6 = 1 : 2 : 2.
Seats in three courses are in the ratio 5 : 6 : 8 and are increased by 20%, 25% and 50% respectively. The new ratio is:
- A. 5 : 6 : 9
- B. 2 : 3 : 4
- C. 6 : 7 : 12
- D. 4 : 5 : 8
Answer: Option D
Explanation:
6 : 7.5 : 12 = 12 : 15 : 24 = 4 : 5 : 8.
Seats in three courses are in the ratio 6 : 5 : 4 and are reduced by 50%, 40% and 25% respectively. The new ratio is:
- A. 1 : 1 : 1
- B. 6 : 5 : 4
- C. 2 : 2 : 1
- D. 3 : 3 : 2
Answer: Option A
Explanation:
3 : 3 : 3 = 1 : 1 : 1.
Boys : girls = 3 : 4. If boys increase by 10% and girls by 20%, the new ratio is:
- A. 13 : 16
- B. 11 : 16
- C. 3 : 4
- D. 33 : 40
Answer: Option B
Explanation:
3.3 : 4.8 = 33 : 48 = 11 : 16.
Boys : girls = 5 : 6. If boys increase by 20% and girls by 25%, the new ratio is:
- A. 4 : 5
- B. 24 : 25
- C. 6 : 7
- D. 5 : 6
Answer: Option A
Explanation:
6 : 7.5 = 4 : 5.
Boys : girls = 4 : 5. If boys increase by 25% and girls by 20%, the new ratio is:
- A. 6 : 5
- B. 5 : 6
- C. 4 : 5
- D. 1 : 1
Answer: Option B
Explanation:
5 : 6.
Boys : girls = 9 : 10. If boys decrease by 10% and girls increase by 20%, the new ratio is:
- A. 81 : 100
- B. 27 : 40
- C. 9 : 10
- D. 3 : 4
Answer: Option B
Explanation:
8.1 : 12 = 81 : 120 = 27 : 40.
Boys : girls = 2 : 3. If boys increase by 50% and girls by 20%, the new ratio is:
- A. 5 : 6
- B. 1 : 1
- C. 2 : 3
- D. 3 : 4
Answer: Option A
Explanation:
3 : 3.6 = 30 : 36 = 5 : 6.
Salaries of A and B are 3 : 5. If each increases by ₹2,000, the ratio becomes 5 : 7. What is B's original salary?
- A. ₹10,000
- B. ₹7,000
- C. ₹5,000
- D. ₹3,000
Answer: Option C
Explanation:
7(3x + 2000) = 5(5x + 2000) → 21x + 14000 = 25x + 10000 → x = 1000; B = 5000.
Salaries of A and B are 4 : 5. If each increases by ₹5,000, the ratio becomes 9 : 11. What is A's original salary?
- A. ₹40,000
- B. ₹50,000
- C. ₹36,000
- D. ₹45,000
Answer: Option A
Explanation:
11(4x + 5000) = 9(5x + 5000) → 44x + 55000 = 45x + 45000 → x = 10000; A = 40,000.
Salaries of A and B are 1 : 2. If each increases by ₹6,000, the ratio becomes 2 : 3. What is B's original salary?
- A. ₹6,000
- B. ₹24,000
- C. ₹18,000
- D. ₹12,000
Answer: Option D
Explanation:
3(x + 6000) = 2(2x + 6000) → x = 6000; B = 12,000.
Salaries of A and B are 5 : 7. If each increases by ₹3,000, the ratio becomes 3 : 4. What is A's NEW salary?
- A. ₹21,000
- B. ₹24,000
- C. ₹18,000
- D. ₹15,000
Answer: Option C
Explanation:
4(5x + 3000) = 3(7x + 3000) → x = 3000; A's new salary = 15,000 + 3,000 = 18,000.
Salaries of A and B are 2 : 5. If each is reduced by ₹1,000, the ratio becomes 1 : 3. What is B's original salary?
- A. ₹8,000
- B. ₹10,000
- C. ₹4,000
- D. ₹12,000
Answer: Option B
Explanation:
3(2x − 1000) = 5x − 1000 → x = 2000; B = 10,000.
If 0.6 : x :: 3 : 7, then x = ?
- A. 2.1
- B. 1.2
- C. 1.4
- D. 0.9
Answer: Option C
Explanation:
3x = 0.6 × 7 = 4.2 → x = 1.4.
If 1.5 : x :: 3 : 4, then x = ?
- A. 1.125
- B. 2.5
- C. 2
- D. 1.8
Answer: Option C
Explanation:
3x = 1.5 × 4 = 6 → x = 2.
If 0.25 : x :: 5 : 12, then x = ?
- A. 0.6
- B. 0.75
- C. 1.2
- D. 0.5
Answer: Option A
Explanation:
5x = 0.25 × 12 = 3 → x = 0.6.
If x : 2.4 :: 3 : 8, then x = ?
- A. 0.8
- B. 6.4
- C. 0.9
- D. 1.2
Answer: Option C
Explanation:
8x = 2.4 × 3 = 7.2 → x = 0.9.
If 0.8 : 1.2 :: x : 4.5, then x = ?
- A. 6.75
- B. 2.5
- C. 3.6
- D. 3
Answer: Option D
Explanation:
1.2x = 0.8 × 4.5 = 3.6 → x = 3.
The sum of three numbers is 170. First : second = 1 : 2 and second : third = 3 : 4. The second number is:
- A. 40
- B. 30
- C. 80
- D. 60
Answer: Option D
Explanation:
A : B : C = 3 : 6 : 8 (17 parts); B = 170 × 6/17 = 60.
The sum of three numbers is 140. First : second = 2 : 3 and second : third = 4 : 5. The third number is:
- A. 60
- B. 48
- C. 45
- D. 32
Answer: Option A
Explanation:
A : B : C = 8 : 12 : 15 (35 parts); C = 140 × 15/35 = 60.
The sum of three numbers is 150. First : second = 3 : 2 and second : third = 3 : 5. The first number is:
- A. 60
- B. 36
- C. 54
- D. 45
Answer: Option C
Explanation:
A : B : C = 9 : 6 : 10 (25 parts); A = 150 × 9/25 = 54.
The sum of three numbers is 99. First : second = 4 : 5 and second : third = 2 : 3. The third number is:
- A. 45
- B. 30
- C. 24
- D. 36
Answer: Option A
Explanation:
A : B : C = 8 : 10 : 15 (33 parts); C = 99 × 15/33 = 45.
The sum of three numbers is 129. First : second = 5 : 6 and second : third = 4 : 7. The first number is:
- A. 63
- B. 30
- C. 25
- D. 36
Answer: Option B
Explanation:
A : B : C = 10 : 12 : 21 (43 parts); A = 129 × 10/43 = 30.
If ₹1,170 is divided in the ratio 1/2 : 1/3 : 1/4, the first part is:
- A. ₹585
- B. ₹270
- C. ₹540
- D. ₹360
Answer: Option C
Explanation:
Ratio = 6 : 4 : 3 (13 parts); first = 1170 × 6/13 = 540.
If ₹1,240 is divided in the ratio 1/2 : 1/3 : 1/5, the second part is:
- A. ₹240
- B. ₹400
- C. ₹413
- D. ₹600
Answer: Option B
Explanation:
Ratio = 15 : 10 : 6 (31 parts); second = 1240 × 10/31 = 400.
If ₹1,100 is divided in the ratio 1/2 : 1/4 : 1/6, the third part is:
- A. ₹183
- B. ₹300
- C. ₹200
- D. ₹600
Answer: Option C
Explanation:
Ratio = 6 : 3 : 2 (11 parts); third = 1100 × 2/11 = 200.
If ₹2,700 is divided in the ratio 1/3 : 1/6 : 1/4, the largest part is:
- A. ₹1,200
- B. ₹1,350
- C. ₹600
- D. ₹900
Answer: Option A
Explanation:
Ratio = 4 : 2 : 3 (9 parts); largest = 2700 × 4/9 = 1200.
If ₹1,500 is divided in the ratio 1/4 : 1/5 : 3/10, the third part is:
- A. ₹450
- B. ₹500
- C. ₹600
- D. ₹400
Answer: Option C
Explanation:
Ratio = 5 : 4 : 6 (15 parts); third = 1500 × 6/15 = 600.
Salaries of A, B, C are 3 : 4 : 5. After increments of 10%, 20% and 30%, the new ratio is:
- A. 3 : 4 : 5
- B. 30 : 48 : 65
- C. 33 : 48 : 65
- D. 33 : 44 : 55
Answer: Option C
Explanation:
3.3 : 4.8 : 6.5 = 33 : 48 : 65.
Salaries of A, B, C are 1 : 2 : 3. After increments of 20%, 15% and 10%, the new ratio is:
- A. 6 : 11 : 15
- B. 1 : 2 : 3
- C. 12 : 23 : 33
- D. 12 : 22 : 33
Answer: Option C
Explanation:
1.2 : 2.3 : 3.3 = 12 : 23 : 33.
Salaries of A, B, C are 4 : 5 : 6. After increments of 25%, 20% and 50%, the new ratio is:
- A. 5 : 6 : 9
- B. 5 : 6 : 8
- C. 4 : 5 : 6
- D. 10 : 12 : 15
Answer: Option A
Explanation:
5 : 6 : 9.
Salaries of A, B, C are 2 : 3 : 4. After increments of 50%, 20% and 25%, the new ratio is:
- A. 6 : 7 : 10
- B. 15 : 18 : 25
- C. 15 : 18 : 20
- D. 3 : 4 : 5
Answer: Option B
Explanation:
3 : 3.6 : 5 = 30 : 36 : 50 = 15 : 18 : 25.
Salaries of A, B, C are 5 : 4 : 3. After increments of 20%, 50% and 100%, the new ratio is:
- A. 2 : 2 : 1
- B. 6 : 6 : 5
- C. 5 : 4 : 3
- D. 1 : 1 : 1
Answer: Option D
Explanation:
6 : 6 : 6 = 1 : 1 : 1.
If 25% of A equals 1/3 of B, then A : B = ?
- A. 3 : 4
- B. 4 : 1
- C. 1 : 3
- D. 4 : 3
Answer: Option D
Explanation:
A/4 = B/3 → A/B = 4/3.
If 20% of A equals 3/4 of B, then A : B = ?
- A. 5 : 3
- B. 3 : 4
- C. 4 : 15
- D. 15 : 4
Answer: Option D
Explanation:
A/5 = 3B/4 → A/B = 15/4.
If 75% of A equals 50% of B, then A : B = ?
- A. 1 : 2
- B. 2 : 3
- C. 3 : 2
- D. 3 : 4
Answer: Option B
Explanation:
3A/4 = B/2 → A/B = 2/3.
If 1/4 of A equals 15% of B, then A : B = ?
- A. 5 : 3
- B. 4 : 15
- C. 3 : 20
- D. 3 : 5
Answer: Option D
Explanation:
A/4 = 3B/20 → A/B = 3/5.
If 12.5% of A equals 1/5 of B, then A : B = ?
- A. 8 : 5
- B. 5 : 2
- C. 5 : 8
- D. 1 : 5
Answer: Option A
Explanation:
A/8 = B/5 → A/B = 8/5.
The fourth proportional to 4, 9, 12 is:
- A. 24
- B. 36
- C. 27
- D. 16
Answer: Option C
Explanation:
4 : 9 :: 12 : x → 4x = 108 → x = 27.
The fourth proportional to 3, 7, 15 is:
- A. 105
- B. 21
- C. 45
- D. 35
Answer: Option D
Explanation:
3 : 7 :: 15 : x → 3x = 105 → x = 35.
The third proportional to 4 and 6 is:
- A. 24
- B. 9
- C. 8
- D. 12
Answer: Option B
Explanation:
4 : 6 :: 6 : x → 4x = 36 → x = 9.
The mean proportional between 9 and 16 is:
- A. 12.5
- B. 12
- C. 25
- D. 144
Answer: Option B
Explanation:
√(9 × 16) = √144 = 12.
The third proportional to 16 and 24 is:
- A. 20
- B. 48
- C. 32
- D. 36
Answer: Option D
Explanation:
16 : 24 :: 24 : x → 16x = 576 → x = 36.
Two numbers are 4 : 7. If 5 is added to each, they become 3 : 5. The smaller number is:
- A. 70
- B. 45
- C. 35
- D. 40
Answer: Option D
Explanation:
5(4x + 5) = 3(7x + 5) → x = 10; smaller = 40.
Two numbers are 5 : 8. If 6 is subtracted from each, they become 1 : 2. The larger number is:
- A. 18
- B. 24
- C. 32
- D. 15
Answer: Option B
Explanation:
2(5x − 6) = 8x − 6 → x = 3; larger = 24.
Two numbers are 2 : 3. If 8 is added to each, they become 3 : 4. The smaller number is:
- A. 16
- B. 24
- C. 18
- D. 12
Answer: Option A
Explanation:
4(2x + 8) = 3(3x + 8) → x = 8; smaller = 16.
Two numbers are 3 : 4. If 5 is subtracted from each, they become 2 : 3. The larger number is:
- A. 15
- B. 20
- C. 16
- D. 25
Answer: Option B
Explanation:
3(3x − 5) = 2(4x − 5) → x = 5; larger = 20.
Two numbers are 5 : 7. If 10 is added to each, they become 3 : 4. The smaller number is:
- A. 40
- B. 70
- C. 50
- D. 30
Answer: Option C
Explanation:
4(5x + 10) = 3(7x + 10) → x = 10; smaller = 50.