Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 593 · 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.₹387 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹344 (b) ₹86 (c) ₹43 (d) ₹301
2. 2.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 39 days (c) 40 days (d) 7 days
3. 3.If 5 notebooks cost ₹70, how much do 9 notebooks cost? (a) ₹140 (b) ₹74 (c) ₹630 (d) ₹126
4. 4.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 18 days (c) 11 days (d) 19 days
5. 5.₹209 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹171 (b) ₹19 (c) ₹57 (d) ₹152
6. 6.If 9 mangoes cost ₹54, how much do 11 mangoes cost? (a) ₹56 (b) ₹594 (c) ₹72 (d) ₹66
7. 7.₹231 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹147 (d) ₹126
8. 8.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹400 (b) ₹325 (c) ₹50 (d) ₹250
9. 9.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 4 days (d) 6 days
10. 10.If 7 kites cost ₹84, how much do 9 kites cost? (a) ₹756 (b) ₹120 (c) ₹108 (d) ₹86
11. 11.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 3 days (d) 5 days
12. 12.If 7 kites cost ₹49, how much do 9 kites cost? (a) ₹441 (b) ₹70 (c) ₹63 (d) ₹51
13. 13.If 4 kites cost ₹56, how much do 2 kites cost? (a) ₹54 (b) ₹112 (c) ₹42 (d) ₹28
14. 14.If 6 notebooks cost ₹36, how much do 10 notebooks cost? (a) ₹40 (b) ₹360 (c) ₹60 (d) ₹66
15. 15.If 2 pens cost ₹20, how much do 3 pens cost? (a) ₹21 (b) ₹40 (c) ₹30 (d) ₹60
16. 16.If 3 pens cost ₹39, how much do 12 pens cost? (a) ₹156 (b) ₹48 (c) ₹169 (d) ₹468
17. 17.₹235 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹141 (b) ₹188 (c) ₹47 (d) ₹94
18. 18.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 18 days (c) 42 days (d) 10 days
19. 19.If 8 notebooks cost ₹104, how much do 4 notebooks cost? (a) ₹416 (b) ₹52 (c) ₹65 (d) ₹100
20. 20.If 8 kites cost ₹64, how much do 9 kites cost? (a) ₹80 (b) ₹65 (c) ₹72 (d) ₹576
21. 21.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 12 days (d) 3 days
22. 22.₹90 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹45 (b) ₹75 (c) ₹90 (d) ₹15
23. 23.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹41 (b) ₹369 (c) ₹328 (d) ₹205
24. 24.If 5 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹36 (b) ₹44 (c) ₹180 (d) ₹45
25. 25.If 2 notebooks cost ₹46, how much do 4 notebooks cost? (a) ₹92 (b) ₹115 (c) ₹184 (d) ₹48
26. 26.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹18 (b) ₹12 (c) ₹24 (d) ₹6
27. 27.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 12 days (d) 6 days
28. 28.If 3 pens cost ₹18, how much do 11 pens cost? (a) ₹26 (b) ₹198 (c) ₹66 (d) ₹72
29. 29.₹360 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹315 (b) ₹360 (c) ₹45 (d) ₹180
30. 30.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 11 days (d) 18 days
31. 31.If 9 kites cost ₹90, how much do 10 kites cost? (a) ₹100 (b) ₹91 (c) ₹110 (d) ₹900
32. 32.If 6 pens cost ₹120, how much do 3 pens cost? (a) ₹80 (b) ₹360 (c) ₹60 (d) ₹117
33. 33.If 7 notebooks cost ₹175, how much do 5 notebooks cost? (a) ₹173 (b) ₹125 (c) ₹875 (d) ₹150
34. 34.₹161 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹23 (b) ₹138 (c) ₹161 (d) ₹139
35. 35.If 5 kites cost ₹120, how much do 10 kites cost? (a) ₹1200 (b) ₹240 (c) ₹125 (d) ₹264
36. 36.If 5 pens cost ₹25, how much do 2 pens cost? (a) ₹22 (b) ₹10 (c) ₹50 (d) ₹15
37. 37.₹112 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹56 (b) ₹28 (c) ₹112 (d) ₹84
38. 38.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
39. 39.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 2 days (d) 1 day
40. 40.If 8 kites cost ₹48, how much do 9 kites cost? (a) ₹432 (b) ₹54 (c) ₹49 (d) ₹60

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