Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 678 · 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.If 7 mangoes cost ₹91, how much do 8 mangoes cost? (a) ₹728 (b) ₹117 (c) ₹104 (d) ₹92
2. 2.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹170 (b) ₹153 (c) ₹68 (d) ₹17
3. 3.₹351 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹156 (d) ₹234
4. 4.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 12 days (d) 19 days
5. 5.₹319 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹29 (b) ₹203 (c) ₹145 (d) ₹174
6. 6.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 3 days (d) 7 days
7. 7.If 4 pens cost ₹12, how much do 5 pens cost? (a) ₹60 (b) ₹15 (c) ₹18 (d) ₹13
8. 8.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 28 days (d) 29 days
9. 9.If 4 kites cost ₹36, how much do 3 kites cost? (a) ₹35 (b) ₹27 (c) ₹108 (d) ₹36
10. 10.If 7 pens cost ₹42, how much do 2 pens cost? (a) ₹84 (b) ₹18 (c) ₹37 (d) ₹12
11. 11.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹198 (b) ₹99 (c) ₹22 (d) ₹176
12. 12.If 4 notebooks cost ₹92, how much do 5 notebooks cost? (a) ₹138 (b) ₹460 (c) ₹93 (d) ₹115
13. 13.If 5 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹44 (b) ₹45 (c) ₹36 (d) ₹180
14. 14.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 42 days (c) 10 days (d) 43 days
15. 15.₹192 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹192 (b) ₹24 (c) ₹168 (d) ₹96
16. 16.If 2 kites cost ₹16, how much do 8 kites cost? (a) ₹64 (b) ₹128 (c) ₹72 (d) ₹22
17. 17.9 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 16 days (d) 10 days
18. 18.If 6 kites cost ₹48, how much do 10 kites cost? (a) ₹480 (b) ₹52 (c) ₹88 (d) ₹80
19. 19.3 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) 3 days (d) 7 days
20. 20.If 2 pens cost ₹16, how much do 8 pens cost? (a) ₹72 (b) ₹64 (c) ₹128 (d) ₹22
21. 21.₹270 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹270 (b) ₹135 (c) ₹240 (d) ₹30
22. 22.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹350 (b) ₹50 (c) ₹250 (d) ₹450
23. 23.₹240 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹120 (b) ₹192 (c) ₹48 (d) ₹240
24. 24.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 49 days (b) 19 days (c) 9 days (d) 4 days
25. 25.If 6 notebooks cost ₹108, how much do 7 notebooks cost? (a) ₹756 (b) ₹126 (c) ₹109 (d) ₹144
26. 26.If 8 pens cost ₹104, how much do 9 pens cost? (a) ₹117 (b) ₹105 (c) ₹130 (d) ₹936
27. 27.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 10 days (d) 7 days
28. 28.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹36 (b) ₹6 (c) ₹30 (d) ₹33
29. 29.₹340 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹238 (b) ₹102 (c) ₹34 (d) ₹170
30. 30.If 8 kites cost ₹184, how much do 7 kites cost? (a) ₹1288 (b) ₹161 (c) ₹184 (d) ₹183
31. 31.If 6 mangoes cost ₹84, how much do 8 mangoes cost? (a) ₹86 (b) ₹672 (c) ₹112 (d) ₹126
32. 32.If 7 pens cost ₹56, how much do 8 pens cost? (a) ₹448 (b) ₹57 (c) ₹72 (d) ₹64
33. 33.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 2 days (d) 8 days
34. 34.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 32 days (c) 3 days (d) 2 days
35. 35.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 8 days (d) 12 days
36. 36.₹104 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹104 (b) ₹13 (c) ₹91 (d) ₹52
37. 37.If 8 kites cost ₹24, how much do 3 kites cost? (a) ₹12 (b) ₹9 (c) ₹72 (d) ₹19
38. 38.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 8 days (c) 6 days (d) 24 days
39. 39.If 3 mangoes cost ₹9, how much do 12 mangoes cost? (a) ₹36 (b) ₹108 (c) ₹39 (d) ₹18
40. 40.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 2 days (d) 3 days

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