Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 668 · 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. 1.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 2 days (d) 8 days
2. 2.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹32 (b) ₹128 (c) ₹144 (d) ₹160
3. 3.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 39 days (d) 40 days
4. 4.₹36 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹18 (b) ₹6 (c) ₹36 (d) ₹30
5. 5.If 4 mangoes cost ₹100, how much do 9 mangoes cost? (a) ₹105 (b) ₹250 (c) ₹225 (d) ₹900
6. 6.If 8 kites cost ₹40, how much do 12 kites cost? (a) ₹44 (b) ₹65 (c) ₹60 (d) ₹480
7. 7.If 2 notebooks cost ₹20, how much do 6 notebooks cost? (a) ₹24 (b) ₹60 (c) ₹70 (d) ₹120
8. 8.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹59 (b) ₹87 (c) ₹29 (d) ₹58
9. 9.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 14 days
10. 10.If 4 pens cost ₹48, how much do 7 pens cost? (a) ₹336 (b) ₹96 (c) ₹84 (d) ₹51
11. 11.₹27 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹19 (b) ₹27 (c) ₹9 (d) ₹18
12. 12.₹110 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹110 (b) ₹22 (c) ₹55 (d) ₹88
13. 13.₹585 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹405 (b) ₹450 (c) ₹45 (d) ₹180
14. 14.If 8 kites cost ₹120, how much do 9 kites cost? (a) ₹1080 (b) ₹121 (c) ₹150 (d) ₹135
15. 15.If 9 mangoes cost ₹90, how much do 10 mangoes cost? (a) ₹100 (b) ₹900 (c) ₹110 (d) ₹91
16. 16.If 9 notebooks cost ₹45, how much do 3 notebooks cost? (a) ₹39 (b) ₹20 (c) ₹15 (d) ₹135
17. 17.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 16 days (d) 15 days
18. 18.If 8 notebooks cost ₹168, how much do 4 notebooks cost? (a) ₹672 (b) ₹84 (c) ₹164 (d) ₹105
19. 19.If 4 mangoes cost ₹60, how much do 10 mangoes cost? (a) ₹150 (b) ₹600 (c) ₹165 (d) ₹66
20. 20.₹392 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹147 (b) ₹49 (c) ₹196 (d) ₹245
21. 21.₹168 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹98 (b) ₹70 (c) ₹14 (d) ₹84
22. 22.₹252 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹196 (b) ₹56 (c) ₹28 (d) ₹126
23. 23.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 24 days (c) 23 days (d) 12 days
24. 24.₹420 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹175 (b) ₹245 (c) ₹210 (d) ₹35
25. 25.₹473 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹387 (b) ₹344 (c) ₹129 (d) ₹43
26. 26.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹250 (b) ₹325 (c) ₹50 (d) ₹400
27. 27.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹174 (b) ₹145 (c) ₹203 (d) ₹29
28. 28.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 33 days (c) 32 days (d) 17 days
29. 29.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 17 days (b) 6 days (c) 4 days (d) 5 days
30. 30.If 3 pens cost ₹66, how much do 6 pens cost? (a) ₹154 (b) ₹69 (c) ₹132 (d) ₹396
31. 31.If 3 pens cost ₹9, how much do 11 pens cost? (a) ₹17 (b) ₹33 (c) ₹36 (d) ₹99
32. 32.5 workers can build a wall in 6 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 12 days (d) 1 day
33. 33.If 4 pens cost ₹80, how much do 2 pens cost? (a) ₹78 (b) ₹160 (c) ₹40 (d) ₹60
34. 34.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 15 days (c) 14 days (d) 4 days
35. 35.8 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 16 days (b) 18 days (c) 8 days (d) 9 days
36. 36.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 14 days (c) 20 days (d) 6 days
37. 37.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 16 days (d) 7 days
38. 38.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 16 days (d) 6 days
39. 39.If 8 pens cost ₹152, how much do 2 pens cost? (a) ₹304 (b) ₹38 (c) ₹57 (d) ₹146
40. 40.If 7 notebooks cost ₹126, how much do 9 notebooks cost? (a) ₹1134 (b) ₹128 (c) ₹180 (d) ₹162

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