Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 723 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 33 days (c) 14 days (d) 32 days
2. 2.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 13 days (d) 20 days
3. 3.If 8 pens cost ₹144, how much do 10 pens cost? (a) ₹180 (b) ₹1440 (c) ₹146 (d) ₹198
4. 4.If 2 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹273 (b) ₹252 (c) ₹52 (d) ₹504
5. 5.If 3 mangoes cost ₹27, how much do 12 mangoes cost? (a) ₹36 (b) ₹324 (c) ₹117 (d) ₹108
6. 6.₹494 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹152 (b) ₹247 (c) ₹342 (d) ₹38
7. 7.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹180 (c) ₹165 (d) ₹30
8. 8.If 6 notebooks cost ₹30, how much do 4 notebooks cost? (a) ₹25 (b) ₹28 (c) ₹20 (d) ₹120
9. 9.₹132 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹66 (b) ₹33 (c) ₹99 (d) ₹132
10. 10.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 52 days (d) 53 days
11. 11.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 1 day
12. 12.If 3 mangoes cost ₹30, how much do 11 mangoes cost? (a) ₹120 (b) ₹110 (c) ₹330 (d) ₹38
13. 13.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 1 day (d) 2 days
14. 14.₹217 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹62 (b) ₹186 (c) ₹155 (d) ₹31
15. 15.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 2 days (d) 18 days
16. 16.If 6 kites cost ₹36, how much do 7 kites cost? (a) ₹37 (b) ₹42 (c) ₹252 (d) ₹48
17. 17.₹385 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹105 (b) ₹315 (c) ₹35 (d) ₹280
18. 18.₹245 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹70 (b) ₹35 (c) ₹175 (d) ₹210
19. 19.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 16 days (c) 9 days (d) 10 days
20. 20.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 6 days (d) 8 days
21. 21.₹35 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹30 (b) ₹10 (c) ₹5 (d) ₹25
22. 22.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 17 days (c) 10 days (d) 16 days
23. 23.₹342 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹38 (b) ₹171 (c) ₹304 (d) ₹342
24. 24.If 5 mangoes cost ₹40, how much do 10 mangoes cost? (a) ₹400 (b) ₹88 (c) ₹80 (d) ₹45
25. 25.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 26 days (b) 16 days (c) 27 days (d) 10 days
26. 26.If 7 kites cost ₹112, how much do 4 kites cost? (a) ₹64 (b) ₹80 (c) ₹448 (d) ₹109
27. 27.If 4 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹49 (b) ₹42 (c) ₹30 (d) ₹168
28. 28.If 6 notebooks cost ₹42, how much do 3 notebooks cost? (a) ₹28 (b) ₹21 (c) ₹39 (d) ₹126
29. 29.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 21 days (d) 22 days
30. 30.If 2 mangoes cost ₹14, how much do 12 mangoes cost? (a) ₹24 (b) ₹168 (c) ₹91 (d) ₹84
31. 31.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 26 days (d) 13 days
32. 32.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 40 days (c) 7 days (d) 39 days
33. 33.If 3 pens cost ₹51, how much do 6 pens cost? (a) ₹306 (b) ₹54 (c) ₹119 (d) ₹102
34. 34.₹198 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹198 (b) ₹33 (c) ₹165 (d) ₹99
35. 35.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 1 day (d) 5 days
36. 36.If 7 pens cost ₹161, how much do 11 pens cost? (a) ₹1771 (b) ₹165 (c) ₹253 (d) ₹276
37. 37.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 5 days (d) 16 days
38. 38.If 7 mangoes cost ₹133, how much do 10 mangoes cost? (a) ₹209 (b) ₹1330 (c) ₹136 (d) ₹190
39. 39.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 21 days (d) 3 days
40. 40.₹48 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹32 (c) ₹48 (d) ₹16

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