Q1): If a:b = 3:5 and b:c = 10:9, what is a:c?
A) 2:3
B) 3:2
C) 5:9
D) 6:5
Answer: A) 2:3
Explanation:
- a:b = 3:5 means a = 3k, b = 5k.
- b:c = 10:9 means b = 10m, c = 9m.
- Make b same in both ratios (common value = 10).
- From 5k = 10, k = 2, so a = 3k = 6.
- From 10m = 10, m = 1, so c = 9m = 9.
- So a:c = 6:9 = 2:3.
Q2): Divide ₹540 in the ratio 2:3:4. What is the largest share?
A) ₹180
B) ₹200
C) ₹220
D) ₹240
Answer: D) ₹240
Explanation:
- Total parts = 2 + 3 + 4 = 9.
- Value of 1 part = 540 ÷ 9 = 60.
- Shares are: 2×60 = 120, 3×60 = 180, 4×60 = 240.
- Largest share = 240.
Q3): If x:(x+4) = 3:5, find x.
A) 4
B) 6
C) 8
D) 10
Answer: B) 6
Explanation:
- x/(x+4) = 3/5.
- Cross-multiply: 5x = 3(x+4).
- Expand: 5x = 3x + 12.
- Subtract 3x: 2x = 12.
- x = 6.
Q4): If A:B = 4:5 and B:C = 6:7, find A:C.
A) 12:35
B) 24:35
C) 20:21
D) 28:30
Answer: B) 24:35
Explanation:
- Make B common in both ratios.
- LCM of 5 and 6 is 30.
- Scale A:B (4:5) by 6 → 24:30.
- Scale B:C (6:7) by 5 → 30:35.
- So A:C = 24:35.
Q5): A 40 L mixture of milk and water is in the ratio 7:3. How much water should be added to make the ratio 7:5?
A) 6 L
B) 8 L
C) 10 L
D) 12 L
Answer: B) 8 L
Explanation:
- Total parts = 7 + 3 = 10.
- Milk = (7/10)×40 = 28 L.
- Water = (3/10)×40 = 12 L.
- New ratio 7:5 means water should be (5/7)×milk.
- Required water = (5/7)×28 = 20 L.
- Water to add = 20 − 12 = 8 L.
Q6): 6 workers finish a work in 15 days. In how many days will 10 workers finish the same work?
A) 6
B) 8
C) 9
D) 10
Answer: C) 9
Explanation:
- Total work (in worker-days) = 6×15 = 90.
- Days needed with 10 workers = 90 ÷ 10.
- Days = 9.
Q7): If 8 kg rice costs ₹360, what is the cost of 13 kg rice?
A) ₹560
B) ₹575
C) ₹585
D) ₹600
Answer: C) ₹585
Explanation:
- Cost per kg = 360 ÷ 8 = 45.
- Cost for 13 kg = 13×45.
- 13×45 = 585.
Q8): In a class, boys:girls = 5:4. If total students are 36, how many girls are there?
A) 14
B) 15
C) 16
D) 18
Answer: C) 16
Explanation:
- Total parts = 5 + 4 = 9.
- 1 part = 36 ÷ 9 = 4.
- Girls = 4 parts = 4×4 = 16.
Q9): Simplify the ratio 0.6:0.9.
A) 2:5
B) 2:3
C) 3:2
D) 6:9
Answer: B) 2:3
Explanation:
- Multiply both by 10 to remove decimals: 0.6:0.9 = 6:9.
- Divide both terms by 3: 6:9 = 2:3.
Q10): Two numbers are in the ratio 3:7. If their difference is 44, find the larger number.
A) 66
B) 70
C) 77
D) 88
Answer: C) 77
Explanation:
- Let numbers be 3x and 7x.
- Difference = 7x − 3x = 4x.
- 4x = 44, so x = 11.
- Larger number = 7x = 7×11 = 77.
Q11): If a:b = 2:3 and b:c = 4:5, find a:b:c.
A) 8:12:15
B) 2:3:5
C) 6:9:10
D) 4:6:5
Answer: A) 8:12:15
Explanation:
- Make b common.
- LCM of 3 and 4 is 12.
- Scale a:b (2:3) by 4 → 8:12.
- Scale b:c (4:5) by 3 → 12:15.
- So a:b:c = 8:12:15.
Q12): If a:b = c:d, and a=18, b=27, c=20, find d.
A) 25
B) 28
C) 30
D) 32
Answer: C) 30
Explanation:
- a/b = c/d.
- 18/27 = 20/d.
- Cross-multiply: 18d = 27×20 = 540.
- d = 540 ÷ 18 = 30.
Q13): The price of sugar increases in the ratio 5:6. To keep expenditure the same, consumption should change in which ratio (old:new)?
A) 5:6
B) 6:5
C) 1:2
D) 11:10
Answer: B) 6:5
Explanation:
- Expenditure = price × consumption.
- If expenditure is constant, consumption is inversely proportional to price.
- Price old:new = 5:6.
- So consumption old:new = 6:5.
Q14): The ratio of ages of A and B is 4:5. After 6 years, it becomes 5:6. Find B’s present age.
A) 24 years
B) 27 years
C) 30 years
D) 33 years
Answer: C) 30 years
Explanation:
- Let A = 4x and B = 5x.
- After 6 years: (4x+6):(5x+6) = 5:6.
- So (4x+6)/(5x+6) = 5/6.
- Cross-multiply: 6(4x+6) = 5(5x+6).
- 24x + 36 = 25x + 30.
- x = 6, so B = 5x = 30.
Q15): On a map, 1 cm represents 5 km. If the distance on the map is 7.5 cm, what is the actual distance?
A) 30 km
B) 35 km
C) 37.5 km
D) 40 km
Answer: C) 37.5 km
Explanation:
- 1 cm corresponds to 5 km.
- 7.5 cm corresponds to 7.5×5 km.
- 7.5×5 = 37.5 km.
Q16): If (x−3):(x+5) = 2:3, find x.
A) 11
B) 13
C) 16
D) 19
Answer: D) 19
Explanation:
- (x−3)/(x+5) = 2/3.
- Cross-multiply: 3(x−3) = 2(x+5).
- Expand: 3x − 9 = 2x + 10.
- x = 19.
Q17): A and B start a business. A invests ₹8000 for 6 months and B invests ₹6000 for 8 months. Total profit is ₹5200. Find A’s share.
A) ₹2400
B) ₹2600
C) ₹2800
D) ₹3000
Answer: B) ₹2600
Explanation:
- Profit share is proportional to (capital × time).
- A’s capital-time = 8000×6 = 48000.
- B’s capital-time = 6000×8 = 48000.
- Ratio A:B = 48000:48000 = 1:1.
- A’s share = 1/(1+1) × 5200 = 2600.
Q18): 12 taps fill a tank in 9 hours. How long will 15 taps take?
A) 6 hours
B) 7.2 hours
C) 7.5 hours
D) 8 hours
Answer: B) 7.2 hours
Explanation:
- Work is constant, so taps × time = constant.
- Total tap-hours = 12×9 = 108.
- Time with 15 taps = 108 ÷ 15.
- 108 ÷ 15 = 7.2 hours.
Q19): Two quantities are in the ratio 5:8. The first increases by 20% and the second decreases by 10%. Find the new ratio.
A) 5:6
B) 6:5
C) 10:13
D) 11:14
Answer: A) 5:6
Explanation:
- Start with values 5 and 8.
- First increases by 20%: 5×1.2 = 6.
- Second decreases by 10%: 8×0.9 = 7.2.
- New ratio = 6:7.2.
- Multiply by 10: 60:72.
- Simplify by 12: 5:6.
Q20): If A:B = 7:9 and B:C = 12:11, find A:B:C in the smallest integers.
A) 21:27:22
B) 28:36:33
C) 35:45:44
D) 14:18:11
Answer: B) 28:36:33
Explanation:
- Make B common.
- LCM of 9 and 12 is 36.
- Scale A:B (7:9) by 4 → 28:36.
- Scale B:C (12:11) by 3 → 36:33.
- So A:B:C = 28:36:33.