Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 952 · 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. 1.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 1 day (d) 10 days
2. 2.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 9 days (d) 11 days
3. 3.If 9 mangoes cost ₹153, how much do 12 mangoes cost? (a) ₹204 (b) ₹1836 (c) ₹221 (d) ₹156
4. 4.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 22 days (d) 15 days
5. 5.If 4 mangoes cost ₹28, how much do 3 mangoes cost? (a) ₹28 (b) ₹27 (c) ₹21 (d) ₹84
6. 6.If 2 notebooks cost ₹38, how much do 10 notebooks cost? (a) ₹190 (b) ₹46 (c) ₹209 (d) ₹380
7. 7.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 1 day (c) 2 days (d) 11 days
8. 8.If 2 pens cost ₹20, how much do 9 pens cost? (a) ₹27 (b) ₹180 (c) ₹100 (d) ₹90
9. 9.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 11 days (d) 17 days
10. 10.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 18 days (d) 9 days
11. 11.If 5 pens cost ₹70, how much do 12 pens cost? (a) ₹840 (b) ₹77 (c) ₹182 (d) ₹168
12. 12.₹406 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹203 (b) ₹145 (c) ₹261 (d) ₹29
13. 13.If 8 pens cost ₹176, how much do 10 pens cost? (a) ₹1760 (b) ₹242 (c) ₹178 (d) ₹220
14. 14.If 6 kites cost ₹90, how much do 9 kites cost? (a) ₹810 (b) ₹135 (c) ₹93 (d) ₹150
15. 15.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 15 days (d) 27 days
16. 16.If 5 notebooks cost ₹70, how much do 8 notebooks cost? (a) ₹73 (b) ₹112 (c) ₹126 (d) ₹560
17. 17.If 5 pens cost ₹45, how much do 2 pens cost? (a) ₹27 (b) ₹42 (c) ₹90 (d) ₹18
18. 18.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 1 day (d) 3 days
19. 19.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 4 days (d) 5 days
20. 20.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹240 (b) ₹200 (c) ₹280 (d) ₹40
21. 21.₹208 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹182 (b) ₹26 (c) ₹104 (d) ₹208
22. 22.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 23 days (d) 22 days
23. 23.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 3 days (d) 2 days
24. 24.If 2 pens cost ₹36, how much do 9 pens cost? (a) ₹43 (b) ₹324 (c) ₹180 (d) ₹162
25. 25.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹46 (b) ₹184 (c) ₹230 (d) ₹138
26. 26.If 8 pens cost ₹184, how much do 7 pens cost? (a) ₹183 (b) ₹184 (c) ₹1288 (d) ₹161
27. 27.₹63 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹63 (b) ₹57 (c) ₹7 (d) ₹56
28. 28.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 1 day (c) 7 days (d) 8 days
29. 29.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 5 days (d) 7 days
30. 30.If 4 mangoes cost ₹84, how much do 5 mangoes cost? (a) ₹85 (b) ₹420 (c) ₹105 (d) ₹126
31. 31.If 9 pens cost ₹216, how much do 4 pens cost? (a) ₹120 (b) ₹96 (c) ₹864 (d) ₹211
32. 32.If 2 mangoes cost ₹42, how much do 12 mangoes cost? (a) ₹273 (b) ₹52 (c) ₹504 (d) ₹252
33. 33.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 3 days (c) 27 days (d) 28 days
34. 34.₹63 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹27 (b) ₹45 (c) ₹36 (d) ₹9
35. 35.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 7 days (d) 2 days
36. 36.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 9 days (d) 2 days
37. 37.₹286 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹110 (b) ₹22 (c) ₹143 (d) ₹176
38. 38.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 3 days (d) 4 days
39. 39.₹400 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹200 (b) ₹350 (c) ₹400 (d) ₹50
40. 40.If 7 notebooks cost ₹161, how much do 4 notebooks cost? (a) ₹644 (b) ₹92 (c) ₹115 (d) ₹158

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