This page gives you 45 Ratio and Proportion questions to practice. Think of it as “number relationships training.” You will work on ratio comparison, proportion, and mixture-style ratios. Every question has an answer with a clear explanation. Solve first, verify later. That’s how speed is built.
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Ratio & Proportion Formulas (Quick Reference)
Symbols (used below):
- a, b, c, x, y, z = quantities/numbers/ages/amounts
- k = constant of proportionality
- m:n = ratio (m parts to n parts)
- Total = sum of all parts
- % = percent (p% = p/100)
- P = profit, I = investment, T = time (months/years)
- LCM = least common multiple, HCF = highest common factor
- | | = absolute value
1) Basics of Ratio
- a:b = m:n means a/b = m/n
- If a:b = m:n, then a = km and b = kn (k is a constant)
- Comparison: a:b = c:d ⇔ ad = bc
2) Ratio After Percentage Change
- If A increases by p%: A’ = A × (1 + p/100)
- If A decreases by p%: A’ = A × (1 − p/100)
- New ratio: A’:B’ = [A × (1 ± p/100)] : [B × (1 ± q/100)]
3) Dividing a Quantity in a Given Ratio
- If total S is divided in ratio m:n: shares are S×m/(m+n) and S×n/(m+n)
- If total S is divided in ratio m:n:p: shares are S×m/(m+n+p), S×n/(m+n+p), S×p/(m+n+p)
- Parts method: 1 part = S ÷ (sum of parts)
4) Combining Ratios (Linking / Chain Rule)
- If a:b = m:n and b:c = p:q, then make b same:
a:b:c = (m×p) : (n×p) : (n×q) - If x:y = m:n and y:z = p:q, then x:z = (m×p) : (n×q)
5) Two Numbers in Ratio with Sum or Difference
- If numbers are in ratio m:n, take them as m k and n k
- If sum is S: (m+n)k = S ⇒ k = S/(m+n)
- If difference is D: |m−n|k = D ⇒ k = D/|m−n|
6) Ages (Ratio Before & After Years)
- If present ages are mk and nk: A = mk, B = nk
- After t years: A+t and B+t
- After t years ratio becomes p:q: (mk+t)/(nk+t) = p/q
7) Mixtures (Adding or Replacing)
- If milk:water = m:n, then milk = mk, water = nk, total = (m+n)k
- After adding water w: new ratio = milk : (water + w)
- After adding milk w: new ratio = (milk + w) : water
- Replacement (remove r and add r): component left = original × (1 − r/Total)
8) Proportion & Variation
- Direct proportion: x ∝ y ⇒ x = ky ⇒ x₁/x₂ = y₁/y₂
- Inverse proportion: x ∝ 1/y ⇒ x = k/y ⇒ x₁/x₂ = y₂/y₁
- Direct & inverse together: x ∝ y/z ⇒ x = k(y/z) ⇒ x₁/x₂ = (y₁/y₂) × (z₂/z₁)
9) Work / Machines / Workers (Proportion Model)
- Work = (workers) × (days) × (rate per worker per day)
- Same work, same rate: W₁D₁ = W₂D₂ (workers × days is constant)
- Machines–Days–Units: Units ∝ (machines × days) ⇒ U₂ = U₁ × (M₂/M₁) × (D₂/D₁)
10) Time & Work (Using Rates)
- If A finishes in x days: rate(A) = 1/x
- If B finishes in y days: rate(B) = 1/y
- Together time: 1/T = 1/x + 1/y ⇒ T = (xy)/(x+y)
11) Partnership (Profit Sharing)
- Profit share ∝ (Investment × Time)
- If A invests I₁ for T₁ and B invests I₂ for T₂: P₁:P₂ = (I₁T₁):(I₂T₂)
- Changing investment mid-way: split time blocks and add:
A effective = I×t + I’×t’
12) Alligation / Mixing Two Percent Solutions
- To mix C₁% and C₂% to get C%: ratio = (C₂ − C) : (C − C₁)
- Works for concentration, profit %, marks %, sugar %, acid %
13) LCM–HCF with Numbers in Ratio
- If numbers are m k and n k (and m, n are coprime):
- HCF = k
- LCM = mnk
- Also: (Number 1) × (Number 2) = HCF × LCM
14) Useful Ratio Transformations
- (a+b):(b+c) when a:b and b:c known:
first convert to a:b:c then compute (a+b) and (b+c) - After transfer/add/subtract: write new amounts, then take ratio
45 Ratio and Proportion Aptitude Questions and Answers
Ratio and Proportion Aptitude Test: Ratio Basics (15 MCQ Questions)
Question 1. The ratio of A:B is 5:7. If A is increased by 20% and B is decreased by 10%, what is the new ratio A:B?
a) 10:11
b) 20:21
c) 5:6
d) 6:7
Answer:
b) 20:21
Question 2. Divide ₹864 in the ratio 5:7:12.
a) ₹180, ₹252, ₹432
b) ₹200, ₹280, ₹384
c) ₹216, ₹288, ₹360
d) ₹240, ₹288, ₹336
Answer:
a) ₹180, ₹252, ₹432
Question 3. If (a:b) = 3:4 and (b:c) = 5:6, find (a:c).
a) 5:8
b) 15:24
c) 9:10
d) 6:5
Answer:
b) 15:24
Question 4. The ratio of two numbers is 7:11 and their difference is 84. Find the smaller number.
a) 147
b) 196
c) 224
d) 308
Answer:
a) 147
Question 5. If 3x:5y = 6:25, find x:y.
a) 2:5
b) 5:2
c) 1:3
d) 3:1
Answer:
a) 2:5
Question 6. The ratio of the present ages of A and B is 4:5. After 6 years, the ratio becomes 5:6. Find A’s present age.
a) 18
b) 20
c) 24
d) 30
Answer:
b) 24
Question 7. If A:B = 2:3 and B:C = 4:5, then A:B:C equals:
a) 8:12:15
b) 2:3:5
c) 8:6:5
d) 4:6:5
Answer:
a) 8:12:15
Question 8. The ratio of milk and water in a mixture is 7:3. If 15 liters of water is added, the ratio becomes 7:5. Find the initial quantity of the mixture.
a) 45 L
b) 60 L
c) 75 L
d) 90 L
Answer:
b) 60 L
Question 9. If A:B = 3:5 and A:C = 4:7, find B:C.
a) 15:28
b) 20:21
c) 35:12
d) 28:15
Answer:
a) 15:28
Question 10. The ratio of two quantities is 9:13. If 24 is added to both, the ratio becomes 3:4. Find the smaller quantity.
a) 72
b) 96
c) 108
d) 144
Answer:
a) 72
Question 11. If x:y = 5:8 and y:z = 12:7, find x:z.
a) 15:7
b) 20:7
c) 25:14
d) 60:56
Answer:
b) 20:7
Question 12. The ratio of salaries of A and B is 7:9. If A’s salary increases by 15% and B’s by 5%, find the new ratio.
a) 161:189
b) 175:189
c) 7:9
d) 23:27
Answer:
a) 161:189
Question 13. A sum of ₹1800 is divided among P, Q, R in the ratio 2:3:4. If Q gives ₹60 to R, what is the new ratio Q:R?
a) 9:14
b) 3:5
c) 11:13
d) 10:11
Answer:
c) 11:13
Question 14. The ratio of boys to girls in a class is 7:5. If 6 girls join the class, the ratio becomes 7:6. Find the initial total students.
a) 60
b) 72
c) 84
d) 96
Answer:
b) 72
Question 15. If A:B = 11:13 and B:C = 26:21, find A:C.
a) 11:21
b) 22:21
c) 13:26
d) 26:33
Answer:
b) 22:21
Ratio and Proportion Aptitude Test: Proportion + Partnership (15 MCQ Questions)
Question 1. If x ∝ y and x = 18 when y = 12, what is x when y = 20?
a) 24
b) 27
c) 30
d) 36
Answer:
c) 30
Question 2. If x ∝ 1/y and x = 15 when y = 6, what is x when y = 10?
a) 6
b) 7.5
c) 9
d) 10
Answer:
b) 9
Question 3. 12 workers can complete a job in 20 days. How many workers are needed to complete it in 15 days?
a) 14
b) 16
c) 18
d) 20
Answer:
b) 16
Question 4. A mixture contains milk and water in the ratio 5:2. If 14 liters of water is added, the ratio becomes 5:4. Find the initial quantity of milk.
a) 35 L
b) 40 L
c) 50 L
d) 60 L
Answer:
c) 50 L
Question 5. Two solutions of sugar in water are 30% and 50% sugar. In what ratio should they be mixed to get a 42% sugar solution?
a) 3:2
b) 2:3
c) 4:1
d) 1:4
Answer:
a) 4:1
Question 6. A invests ₹12000 for 8 months, B invests ₹15000 for 6 months, and C invests ₹18000 for 4 months. Find the ratio of their profits.
a) 16:15:12
b) 8:9:12
c) 16:15:12
d) 12:15:16
Answer:
a) 16:15:12
Question 7. A, B, and C start a business. A invests ₹40,000, B invests ₹50,000. After 6 months, C joins with ₹60,000. At the end of 1 year, profits are shared in what ratio?
a) 4:5:6
b) 8:10:6
c) 8:10:12
d) 6:5:4
Answer:
b) 8:10:6
Question 8. A mixture has alcohol and water in ratio 7:3. If 10 liters of mixture is replaced with 10 liters water, the ratio becomes 7:5. Find initial quantity of mixture.
a) 40 L
b) 50 L
c) 60 L
d) 70 L
Answer:
c) 60 L
Question 9. If 15 machines can produce 600 units in 8 days, how many units will 20 machines produce in 12 days?
a) 1000
b) 1200
c) 1500
d) 1800
Answer:
b) 1200
Question 10. A can do a work in 18 days and B can do it in 27 days. If they work together, in how many days will they finish the work?
a) 9
b) 10
c) 11
d) 12
Answer:
b) 10
Question 11. A and B invest in ratio 3:5. After 4 months, A doubles his investment. If total profit after 1 year is ₹96,000, find B’s share.
a) ₹52,800
b) ₹54,000
c) ₹57,600
d) ₹60,000
Answer:
c) ₹57,600
Question 12. In how many ways can 20 liters of 25% acid solution be mixed with x liters of 40% acid solution to get 30% acid solution?
a) 5
b) 10
c) 15
d) 20
Answer:
b) 10
Question 13. If a:b = 4:7 and b:c = 9:5, then (a+b):(b+c) equals:
a) 99:98
b) 64:77
c) 73:68
d) 45:56
Answer:
a) 99:98
Question 14. A sum is divided among A, B, C in ratio 5:7:8. If C gets ₹240 more than A, find the total sum.
a) ₹1200
b) ₹1440
c) ₹1600
d) ₹1800
Answer:
b) ₹1440
Question 15. If x varies directly as y and inversely as z. If x = 12 when y = 8 and z = 4, find x when y = 15 and z = 10.
a) 4.5
b) 5.25
c) 6
d) 7.5
Answer:
b) 4.5
Ratio and Proportion Aptitude Test: Word Problems (Exam-grade) (15 MCQ Questions)
Question 1. The ratio of ages of A and B is 3:5. After 8 years, the ratio becomes 5:7. Find A’s present age.
a) 18
b) 21
c) 24
d) 27
Answer:
c) 24
Question 2. A sum of money is divided among P, Q, R. P gets 1/4 of the total, Q gets 2/5 of the remaining, and R gets the rest. Find the ratio P:Q:R.
a) 5:6:9
b) 5:9:6
c) 3:5:7
d) 2:3:5
Answer:
a) 5:6:9
Question 3. The ratio of two numbers is 4:9. If 15 is added to both, the ratio becomes 1:2. Find the smaller number.
a) 20
b) 24
c) 28
d) 36
Answer:
b) 24
Question 4. The incomes of A and B are in ratio 5:7 and their expenditures are in ratio 3:4. If each saves ₹2000, find their incomes.
a) ₹10000 and ₹14000
b) ₹12000 and ₹16800
c) ₹15000 and ₹21000
d) Cannot be determined
Answer:
d) Cannot be determined
Question 5. A and B have money in ratio 7:9. If A gives ₹240 to B, the ratio becomes 5:11. Find the total money they had initially.
a) ₹2400
b) ₹3000
c) ₹3600
d) ₹4200
Answer:
b) ₹3000
Question 6. A mixture of tea contains tea and sugar in ratio 12:1. If 10 kg sugar is added, the ratio becomes 12:2. Find the initial quantity of tea.
a) 100 kg
b) 120 kg
c) 140 kg
d) 240 kg
Answer:
b) 120 kg
Question 7. The ratio of lengths of two rods is 5:8 and their weights are in ratio 3:5. Find the ratio of their densities (density = weight/volume, and volume ∝ length for same cross-section).
a) 24:25
b) 15:16
c) 9:10
d) 5:3
Answer:
a) 24:25
Question 8. Two numbers are in ratio 3:7. If their LCM is 840, find their HCF.
a) 20
b) 30
c) 40
d) 60
Answer:
b) 30
Question 9. A and B together have ₹8400. If A’s money is 20% less than B’s, find A:B.
a) 4:5
b) 5:6
c) 6:7
d) 7:8
Answer:
a) 4:5
Question 10. The ratio of prices of apples and oranges is 3:2. If 2 kg apples and 3 kg oranges cost ₹420, find the cost of 1 kg apples.
a) ₹90
b) ₹100
c) ₹120
d) ₹140
Answer:
c) ₹120
Question 11. DATA SUFFICIENCY: Find the ratio of A’s age to B’s age.
I. A is 6 years older than B.
II. After 6 years, A:B will be 5:4.
a) Statement I alone is sufficient
b) Statement II alone is sufficient
c) Both statements together are sufficient, but neither alone
d) Even together, not sufficient
Answer:
c) Both statements together are sufficient, but neither alone
Question 12. DATA SUFFICIENCY: Find the ratio of amounts of milk and water in the mixture.
I. If 10 L water is added, the ratio becomes 3:2.
II. If 8 L milk is added, the ratio becomes 5:2.
a) Statement I alone is sufficient
b) Statement II alone is sufficient
c) Both statements together are sufficient, but neither alone
d) Even together, not sufficient
Answer:
c) Both statements together are sufficient, but neither alone
Question 13. DATA SUFFICIENCY: Find the ratio of investments of A and B.
I. Profit share ratio is 3:4.
II. A invested for 9 months and B invested for 6 months.
a) Statement I alone is sufficient
b) Statement II alone is sufficient
c) Both statements together are sufficient, but neither alone
d) Even together, not sufficient
Answer:
c) Both statements together are sufficient, but neither alone
Question 14. A sum is divided among A, B, C in ratio 2:3:5. If B and C together get ₹480 more than A, find A’s share.
a) ₹180
b) ₹240
c) ₹300
d) ₹360
Answer:
c) ₹300
Question 15. The ratio of the number of students in classes X, Y, Z is 4:5:6. If 30 students are moved from Z to X, the ratio becomes 5:5:5. Find total number of students initially.
a) 300
b) 330
c) 360
d) 390
Answer:
c) 360
