Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 126 · 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.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹72 (b) ₹48 (c) ₹24 (d) ₹36
2. 2.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 7 days
3. 3.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 23 days (c) 12 days (d) 25 days
4. 4.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 1 day (c) 9 days (d) 8 days
5. 5.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 34 days (c) 7 days (d) 15 days
6. 6.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 16 days (c) 11 days (d) 13 days
7. 7.If 7 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹58 (b) ₹126 (c) ₹27 (d) ₹18
8. 8.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 20 days (b) 21 days (c) 14 days (d) 16 days
9. 9.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 32 days (c) 14 days (d) 33 days
10. 10.₹210 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹135 (d) ₹105
11. 11.If 5 notebooks cost ₹50, how much do 3 notebooks cost? (a) ₹48 (b) ₹40 (c) ₹30 (d) ₹150
12. 12.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹116 (b) ₹145 (c) ₹29 (d) ₹87
13. 13.If 3 kites cost ₹9, how much do 10 kites cost? (a) ₹90 (b) ₹30 (c) ₹16 (d) ₹33
14. 14.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 49 days (c) 4 days (d) 9 days
15. 15.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 23 days (b) 14 days (c) 8 days (d) 22 days
16. 16.If 7 notebooks cost ₹126, how much do 2 notebooks cost? (a) ₹121 (b) ₹36 (c) ₹252 (d) ₹54
17. 17.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹39 (b) ₹156 (c) ₹78 (d) ₹117
18. 18.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 10 days (d) 9 days
19. 19.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹350 (b) ₹35 (c) ₹140 (d) ₹315
20. 20.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 9 days (d) 8 days
21. 21.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹32 (c) ₹192 (d) ₹160
22. 22.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 18 days (d) 8 days
23. 23.If 8 kites cost ₹24, how much do 2 kites cost? (a) ₹48 (b) ₹9 (c) ₹18 (d) ₹6
24. 24.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹99 (d) ₹11
25. 25.If 2 mangoes cost ₹8, how much do 6 mangoes cost? (a) ₹28 (b) ₹24 (c) ₹48 (d) ₹12
26. 26.If 8 pens cost ₹160, how much do 11 pens cost? (a) ₹240 (b) ₹220 (c) ₹163 (d) ₹1760
27. 27.If 5 notebooks cost ₹80, how much do 10 notebooks cost? (a) ₹800 (b) ₹85 (c) ₹176 (d) ₹160
28. 28.If 3 pens cost ₹9, how much do 5 pens cost? (a) ₹45 (b) ₹11 (c) ₹15 (d) ₹18
29. 29.If 9 mangoes cost ₹171, how much do 12 mangoes cost? (a) ₹174 (b) ₹228 (c) ₹2052 (d) ₹247
30. 30.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 1 day (c) 11 days (d) 10 days
31. 31.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 3 days (d) 2 days
32. 32.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹11 (d) ₹66
33. 33.₹117 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹105 (b) ₹104 (c) ₹13 (d) ₹117
34. 34.If 3 mangoes cost ₹27, how much do 7 mangoes cost? (a) ₹63 (b) ₹72 (c) ₹31 (d) ₹189
35. 35.If 6 pens cost ₹108, how much do 12 pens cost? (a) ₹1296 (b) ₹114 (c) ₹234 (d) ₹216
36. 36.If 5 pens cost ₹75, how much do 2 pens cost? (a) ₹30 (b) ₹72 (c) ₹150 (d) ₹45
37. 37.If 6 notebooks cost ₹42, how much do 2 notebooks cost? (a) ₹21 (b) ₹38 (c) ₹84 (d) ₹14
38. 38.If 3 kites cost ₹69, how much do 4 kites cost? (a) ₹92 (b) ₹115 (c) ₹276 (d) ₹70
39. 39.If 5 notebooks cost ₹95, how much do 10 notebooks cost? (a) ₹100 (b) ₹209 (c) ₹190 (d) ₹950
40. 40.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 19 days (c) 7 days (d) 40 days

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