Arithmetics Questions From Ratio & Proportions-1

প্রারম্ভিক গণিত বিষয়টি প্রতিযোগিতামূলক বিভিন্ন পরীক্ষায় একটি গুরুত্বপূর্ণ বিষয় । প্রায় প্রতিটি পরীক্ষাতেই গণিত থেকে কমবেশি প্রশ্ন আসে । প্রতিযোগিতামূলক পরীক্ষায় সাফল্যের মোড় ঘুরিয়ে দেওয়ার ক্ষেত্রে গণিত প্রশ্নগুলি ল্যান্ডমার্ক এর ভূমিকা পালন করে । তাই প্রস্তুতির প্রথম থেকে গণিতের প্রতি যত্ন নেওয়ার কাজ এগিয়ে নিয়ে যেতে এখন থেকেই প্র্যাকটিস করুন আমাদের সাথে । এখন থাকছে Arithmetics Questions From Ratio & Proportions-1

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Arithmetics Questions From Ratio & Proportions-1

⟽ Previous Set

1. If 3:4 = 5:x, then x =
3/4 = 5/x
3x = 4 × 5
x = 20/3
Answer: 20/3

2. The ratio of the ages of A and B is 5:7. If the sum of their ages is 60, how old is A?
A:B = 5:7
5 + 7 = 12
A = (5/12) × 60
= 25
Answer: 25

3. If x:y = 2:3 and y:z = 4:5, then x:y:z =
x:y = 2:3 = 8:12
y:z = 4:5 = 12:15
x:y:z = 8:12:15
Answer: 8:12:15

4. A mixture contains milk and water in the ratio 3:2. If 10 liters of milk is added, the ratio becomes 2:1. How many liters of water are there?
Milk:Water = 3:2
Let milk = 3x, water = 2x
(3x + 10)/2x = 2/1
3x + 10 = 4x
x = 10
Water = 2x = 2 × 10 = 20
Answer: 20

5. If a:b = 2:3 and b:c = 5:7, then a:c =
a:b = 2:3
b:c = 5:7 = 3:(21/5)
a:c = 2:(21/5)
= 10:21
Answer: 10:21

6. The ratio of the speeds of two trains is 3:4. If the first train covers 240 km in 4 hours, how far does the second train cover in 3 hours?
Speed of first train = 240/4 = 60 km/h
Speed of second train = (4/3) × 60 = 80 km/h
Distance = 80 × 3 = 240 km
Answer: 240 km

7. If x:y = 3:4 and y:z = 5:6, then x:z =
x:y = 3:4
y:z = 5:6 = 4:(24/5)
x:z = 3:(24/5)
= 15:24
Answer: 15:24

8. A sum of ₹1200 is divided among A, B, and C in the ratio 2:3:5. How much does A get?
A:B:C = 2:3:5
2 + 3 + 5 = 10
A = (2/10) × 1200
= ₹240
Answer: ₹240

9. If a:b = 4:5 and b:c = 3:2, then a:b:c =
a:b = 4:5 = 12:15
b:c = 3:2 = 15:10
a:b:c = 12:15:10
Answer: 12:15:10

10. The ratio of the ages of A and B is 5:7. If A is 25 years old, how old is B?
A:B = 5:7
5 → 25
7 → ?
B = (7/5) × 25
= 35
Answer: 35

11. If x:y = 2:3 and y:z = 4:5, then x:y:z =
x:y = 2:3 = 8:12
y:z = 4:5 = 12:15
x:y:z = 8:12:15
Answer: 8:12:15

12. A mixture contains acid and water in the ratio 1:3. If 10 liters of acid is added, the ratio becomes 1:2. How many liters of water are there?
Acid:Water = 1:3
Let acid = x, water = 3x
(x + 10)/3x = 1/2
2x + 20 = 3x
x = 20
Water = 3x = 3 × 10 = 30
Answer: 30

13. If a:b = 3:4 and b:c = 5:6, then a:c =
a:b = 3:4
b:c = 5:6 = 4:(24/5)
a:c = 3:(24/5)
= 15:24
Answer: 15:24

14. The ratio of the speeds of two cars is 2:3. If the first car covers 120 km in 2 hours, how far does the second car cover in 3 hours?
Speed of first car = 120/2 = 60 km/h
Speed of second car = (3/2) × 60 = 90 km/h
Distance = 90 × 3 = 270 km
Answer: 270 km

15. If x:y = 5:6 and y:z = 7:8, then x:y:z =
x:y = 5:6 = 35:42
y:z = 7:8 = 42:48
x:y:z = 35:42:48
Answer: 35:42:48

16. A sum of ₹1500 is divided among A, B, and C in the ratio 3:4:5. How much does B get?
A:B:C = 3:4:5
3 + 4 + 5 = 12
B = (4/12) × 1500
= ₹500
Answer: ₹500

17. If a:b = 2:3 and b:c = 4:5, then a:b:c =
a:b = 2:3 = 8:12
b:c = 4:5 = 12:15
a:b:c = 8:12:15
Answer: 8:12:15

18. The ratio of the ages of A and B is 4:5. If B is 30 years old, how old is A?
A:B = 4:5
5 → 30
4 → ?
A = (4/5) × 30
= 24
Answer: 24

19. If x:y = 3:4 and y:z = 5:6, then x:z =
x:y = 3:4
y:z = 5:6 = 4:(24/5)
x:z = 3:(24/5)
= 15:24
Answer: 15:24

20. A mixture contains milk and water in the ratio 2:3. If 10 liters of milk is added, the ratio becomes 3:2. How many liters of water are there?
Milk:Water = 2:3
Let milk = 2x, water = 3x
(2x + 10)/3x = 3/2
4x + 20 = 9x
5x = 20
x = 4 Arithmetics Questions From Ratio
Water = 3x = 3 × 4 = 12
Answer: 12  ➣ Next Set

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