Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 687 · 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. 1.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 3 days (d) 4 days
2. 2.If 5 pens cost ₹115, how much do 10 pens cost? (a) ₹1150 (b) ₹120 (c) ₹230 (d) ₹253
3. 3.If 3 notebooks cost ₹21, how much do 11 notebooks cost? (a) ₹231 (b) ₹29 (c) ₹84 (d) ₹77
4. 4.If 8 notebooks cost ₹120, how much do 5 notebooks cost? (a) ₹117 (b) ₹75 (c) ₹600 (d) ₹90
5. 5.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹10 (b) ₹60 (c) ₹70 (d) ₹50
6. 6.If 5 kites cost ₹25, how much do 3 kites cost? (a) ₹20 (b) ₹75 (c) ₹15 (d) ₹23
7. 7.If 9 mangoes cost ₹198, how much do 6 mangoes cost? (a) ₹1188 (b) ₹195 (c) ₹132 (d) ₹154
8. 8.If 7 pens cost ₹91, how much do 9 pens cost? (a) ₹130 (b) ₹117 (c) ₹819 (d) ₹93
9. 9.If 4 mangoes cost ₹92, how much do 8 mangoes cost? (a) ₹207 (b) ₹96 (c) ₹184 (d) ₹736
10. 10.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 1 day (d) 22 days
11. 11.If 3 pens cost ₹66, how much do 9 pens cost? (a) ₹198 (b) ₹220 (c) ₹594 (d) ₹72
12. 12.If 3 mangoes cost ₹39, how much do 2 mangoes cost? (a) ₹39 (b) ₹26 (c) ₹78 (d) ₹38
13. 13.₹128 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹128 (b) ₹64 (c) ₹96 (d) ₹32
14. 14.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹80 (b) ₹70 (c) ₹40 (d) ₹10
15. 15.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹400 (b) ₹200 (c) ₹40 (d) ₹360
16. 16.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 3 days (d) 9 days
17. 17.₹184 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹184 (d) ₹92
18. 18.If 3 pens cost ₹48, how much do 6 pens cost? (a) ₹288 (b) ₹96 (c) ₹51 (d) ₹112
19. 19.If 8 pens cost ₹200, how much do 4 pens cost? (a) ₹196 (b) ₹125 (c) ₹800 (d) ₹100
20. 20.If 7 pens cost ₹126, how much do 11 pens cost? (a) ₹130 (b) ₹1386 (c) ₹198 (d) ₹216
21. 21.₹301 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹86 (b) ₹43 (c) ₹258 (d) ₹215
22. 22.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 9 days (d) 45 days
23. 23.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 16 days (c) 15 days (d) 9 days
24. 24.If 7 kites cost ₹35, how much do 6 kites cost? (a) ₹34 (b) ₹210 (c) ₹35 (d) ₹30
25. 25.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 7 days (d) 39 days
26. 26.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹165 (b) ₹33 (c) ₹297 (d) ₹264
27. 27.If 3 mangoes cost ₹18, how much do 4 mangoes cost? (a) ₹72 (b) ₹30 (c) ₹24 (d) ₹19
28. 28.If 7 notebooks cost ₹77, how much do 2 notebooks cost? (a) ₹72 (b) ₹33 (c) ₹22 (d) ₹154
29. 29.₹81 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹73 (b) ₹81 (c) ₹72 (d) ₹9
30. 30.If 2 kites cost ₹38, how much do 9 kites cost? (a) ₹342 (b) ₹171 (c) ₹45 (d) ₹190
31. 31.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 3 days (c) 11 days (d) 7 days
32. 32.If 2 notebooks cost ₹22, how much do 3 notebooks cost? (a) ₹23 (b) ₹33 (c) ₹66 (d) ₹44
33. 33.If 2 notebooks cost ₹40, how much do 3 notebooks cost? (a) ₹41 (b) ₹60 (c) ₹80 (d) ₹120
34. 34.₹48 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹8 (b) ₹24 (c) ₹48 (d) ₹40
35. 35.If 3 pens cost ₹24, how much do 5 pens cost? (a) ₹120 (b) ₹48 (c) ₹40 (d) ₹26
36. 36.₹330 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹165 (b) ₹33 (c) ₹297 (d) ₹330
37. 37.If 9 notebooks cost ₹171, how much do 2 notebooks cost? (a) ₹342 (b) ₹38 (c) ₹57 (d) ₹164
38. 38.If 6 kites cost ₹150, how much do 2 kites cost? (a) ₹50 (b) ₹146 (c) ₹300 (d) ₹75
39. 39.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 26 days (c) 27 days (d) 9 days
40. 40.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹82 (b) ₹287 (c) ₹328 (d) ₹41

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