Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 755 · 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. 1.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 34 days (c) 33 days (d) 17 days
2. 2.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 8 days (d) 7 days
3. 3.₹253 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹23 (b) ₹184 (c) ₹207 (d) ₹69
4. 4.If 4 mangoes cost ₹36, how much do 7 mangoes cost? (a) ₹39 (b) ₹72 (c) ₹252 (d) ₹63
5. 5.If 7 mangoes cost ₹28, how much do 4 mangoes cost? (a) ₹20 (b) ₹16 (c) ₹25 (d) ₹112
6. 6.If 7 notebooks cost ₹91, how much do 12 notebooks cost? (a) ₹1092 (b) ₹96 (c) ₹156 (d) ₹169
7. 7.If 8 pens cost ₹200, how much do 10 pens cost? (a) ₹250 (b) ₹2000 (c) ₹275 (d) ₹202
8. 8.₹180 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹30 (b) ₹180 (c) ₹150 (d) ₹90
9. 9.If 6 pens cost ₹84, how much do 7 pens cost? (a) ₹85 (b) ₹588 (c) ₹112 (d) ₹98
10. 10.If 4 pens cost ₹12, how much do 11 pens cost? (a) ₹19 (b) ₹33 (c) ₹132 (d) ₹36
11. 11.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 16 days (d) 20 days
12. 12.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 11 days (d) 10 days
13. 13.If 6 mangoes cost ₹120, how much do 5 mangoes cost? (a) ₹119 (b) ₹100 (c) ₹600 (d) ₹120
14. 14.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 24 days (c) 25 days (d) 14 days
15. 15.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹200 (b) ₹275 (c) ₹350 (d) ₹50
16. 16.If 6 pens cost ₹18, how much do 8 pens cost? (a) ₹27 (b) ₹144 (c) ₹24 (d) ₹20
17. 17.If 6 pens cost ₹60, how much do 8 pens cost? (a) ₹480 (b) ₹80 (c) ₹62 (d) ₹90
18. 18.₹350 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹50 (b) ₹150 (c) ₹200 (d) ₹175
19. 19.4 workers can build a wall in 9 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 6 days (d) 7 days
20. 20.If 2 pens cost ₹48, how much do 12 pens cost? (a) ₹288 (b) ₹312 (c) ₹58 (d) ₹576
21. 21.If 4 notebooks cost ₹28, how much do 12 notebooks cost? (a) ₹36 (b) ₹336 (c) ₹84 (d) ₹91
22. 22.₹190 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹95 (b) ₹190 (c) ₹19 (d) ₹171
23. 23.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹17 (b) ₹153 (c) ₹34 (d) ₹170
24. 24.₹275 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹225 (b) ₹50 (c) ₹25 (d) ₹250
25. 25.If 8 pens cost ₹48, how much do 3 pens cost? (a) ₹43 (b) ₹144 (c) ₹18 (d) ₹24
26. 26.If 7 mangoes cost ₹56, how much do 4 mangoes cost? (a) ₹40 (b) ₹224 (c) ₹32 (d) ₹53
27. 27.If 4 notebooks cost ₹68, how much do 12 notebooks cost? (a) ₹76 (b) ₹816 (c) ₹221 (d) ₹204
28. 28.If 5 mangoes cost ₹70, how much do 7 mangoes cost? (a) ₹490 (b) ₹98 (c) ₹72 (d) ₹112
29. 29.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 4 days (c) 36 days (d) 6 days
30. 30.If 5 notebooks cost ₹90, how much do 2 notebooks cost? (a) ₹87 (b) ₹36 (c) ₹180 (d) ₹54
31. 31.₹136 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹68 (b) ₹136 (c) ₹34 (d) ₹102
32. 32.If 8 pens cost ₹72, how much do 4 pens cost? (a) ₹45 (b) ₹288 (c) ₹36 (d) ₹68
33. 33.If 5 mangoes cost ₹45, how much do 6 mangoes cost? (a) ₹270 (b) ₹63 (c) ₹46 (d) ₹54
34. 34.If 3 pens cost ₹33, how much do 7 pens cost? (a) ₹37 (b) ₹88 (c) ₹231 (d) ₹77
35. 35.If 9 kites cost ₹72, how much do 5 kites cost? (a) ₹360 (b) ₹48 (c) ₹40 (d) ₹68
36. 36.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 30 days (b) 13 days (c) 17 days (d) 31 days
37. 37.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹43 (b) ₹301 (c) ₹258 (d) ₹215
38. 38.If 3 mangoes cost ₹21, how much do 7 mangoes cost? (a) ₹147 (b) ₹56 (c) ₹49 (d) ₹25
39. 39.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 48 days (d) 18 days
40. 40.If 9 pens cost ₹135, how much do 8 pens cost? (a) ₹1080 (b) ₹134 (c) ₹120 (d) ₹135

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