Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 748 · 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 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 11 days (d) 12 days
2. 2.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 15 days (d) 14 days
3. 3.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹88 (b) ₹16 (c) ₹80 (d) ₹96
4. 4.If 5 mangoes cost ₹110, how much do 6 mangoes cost? (a) ₹132 (b) ₹111 (c) ₹660 (d) ₹154
5. 5.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 35 days (c) 19 days (d) 36 days
6. 6.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 7 days (d) 3 days
7. 7.₹55 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹45 (b) ₹15 (c) ₹40 (d) ₹5
8. 8.₹84 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹54 (b) ₹30 (c) ₹42 (d) ₹6
9. 9.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 14 days
10. 10.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 6 days
11. 11.₹390 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹273 (b) ₹117 (c) ₹39 (d) ₹195
12. 12.If 5 notebooks cost ₹125, how much do 2 notebooks cost? (a) ₹122 (b) ₹250 (c) ₹75 (d) ₹50
13. 13.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹275 (b) ₹300 (c) ₹250 (d) ₹50
14. 14.₹429 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹297 (b) ₹264 (c) ₹33 (d) ₹165
15. 15.If 6 kites cost ₹36, how much do 7 kites cost? (a) ₹48 (b) ₹42 (c) ₹252 (d) ₹37
16. 16.If 8 mangoes cost ₹184, how much do 12 mangoes cost? (a) ₹2208 (b) ₹299 (c) ₹276 (d) ₹188
17. 17.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 11 days (d) 12 days
18. 18.If 3 kites cost ₹18, how much do 4 kites cost? (a) ₹24 (b) ₹19 (c) ₹72 (d) ₹30
19. 19.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹184 (d) ₹138
20. 20.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹47 (c) ₹376 (d) ₹235
21. 21.If 3 pens cost ₹57, how much do 12 pens cost? (a) ₹66 (b) ₹247 (c) ₹684 (d) ₹228
22. 22.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 1 day
23. 23.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 11 days (d) 7 days
24. 24.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 6 days
25. 25.If 8 pens cost ₹88, how much do 7 pens cost? (a) ₹87 (b) ₹77 (c) ₹88 (d) ₹616
26. 26.If 3 pens cost ₹60, how much do 6 pens cost? (a) ₹360 (b) ₹63 (c) ₹120 (d) ₹140
27. 27.If 3 mangoes cost ₹9, how much do 4 mangoes cost? (a) ₹10 (b) ₹12 (c) ₹36 (d) ₹15
28. 28.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 53 days (c) 7 days (d) 52 days
29. 29.₹434 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹217 (b) ₹31 (c) ₹155 (d) ₹279
30. 30.If 7 notebooks cost ₹35, how much do 3 notebooks cost? (a) ₹105 (b) ₹15 (c) ₹20 (d) ₹31
31. 31.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 3 days (d) 6 days
32. 32.₹189 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹108 (b) ₹81 (c) ₹27 (d) ₹135
33. 33.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 28 days (b) 8 days (c) 7 days (d) 20 days
34. 34.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 15 days (d) 13 days
35. 35.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 17 days (c) 46 days (d) 45 days
36. 36.If 9 mangoes cost ₹207, how much do 7 mangoes cost? (a) ₹1449 (b) ₹161 (c) ₹205 (d) ₹184
37. 37.₹189 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹169 (b) ₹21 (c) ₹168 (d) ₹189
38. 38.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 3 days (d) 18 days
39. 39.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 22 days (c) 15 days (d) 7 days
40. 40.₹270 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹243 (b) ₹270 (c) ₹27 (d) ₹135

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