Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 371 · 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. 1.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 12 days (c) 23 days (d) 25 days
2. 2.If 9 notebooks cost ₹54, how much do 11 notebooks cost? (a) ₹594 (b) ₹66 (c) ₹56 (d) ₹72
3. 3.If 8 notebooks cost ₹88, how much do 9 notebooks cost? (a) ₹792 (b) ₹89 (c) ₹99 (d) ₹110
4. 4.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹6 (b) ₹15 (c) ₹12 (d) ₹18
5. 5.If 6 kites cost ₹132, how much do 4 kites cost? (a) ₹130 (b) ₹528 (c) ₹110 (d) ₹88
6. 6.If 4 notebooks cost ₹12, how much do 9 notebooks cost? (a) ₹30 (b) ₹17 (c) ₹108 (d) ₹27
7. 7.₹77 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹35 (c) ₹7 (d) ₹49
8. 8.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹35 (d) ₹40
9. 9.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 20 days (c) 8 days (d) 56 days
10. 10.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹25 (b) ₹20 (c) ₹5 (d) ₹30
11. 11.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 5 days
12. 12.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 2 days (c) 8 days (d) 3 days
13. 13.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 3 days (d) 2 days
14. 14.₹105 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹21 (b) ₹105 (c) ₹84 (d) ₹85
15. 15.₹65 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹39 (b) ₹26 (c) ₹13 (d) ₹52
16. 16.If 2 kites cost ₹42, how much do 3 kites cost? (a) ₹126 (b) ₹43 (c) ₹63 (d) ₹84
17. 17.If 6 pens cost ₹24, how much do 4 pens cost? (a) ₹96 (b) ₹20 (c) ₹22 (d) ₹16
18. 18.If 5 pens cost ₹70, how much do 8 pens cost? (a) ₹560 (b) ₹112 (c) ₹73 (d) ₹126
19. 19.₹174 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹87 (b) ₹174 (c) ₹29 (d) ₹145
20. 20.If 2 notebooks cost ₹28, how much do 9 notebooks cost? (a) ₹140 (b) ₹126 (c) ₹35 (d) ₹252
21. 21.If 9 mangoes cost ₹36, how much do 8 mangoes cost? (a) ₹35 (b) ₹288 (c) ₹36 (d) ₹32
22. 22.If 3 kites cost ₹39, how much do 9 kites cost? (a) ₹130 (b) ₹45 (c) ₹351 (d) ₹117
23. 23.If 3 pens cost ₹21, how much do 9 pens cost? (a) ₹27 (b) ₹189 (c) ₹63 (d) ₹70
24. 24.₹315 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹281 (b) ₹315 (c) ₹280 (d) ₹35
25. 25.₹63 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹21 (c) ₹42 (d) ₹63
26. 26.If 4 notebooks cost ₹76, how much do 3 notebooks cost? (a) ₹76 (b) ₹57 (c) ₹75 (d) ₹228
27. 27.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 25 days (d) 24 days
28. 28.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹144 (b) ₹160 (c) ₹16 (d) ₹80
29. 29.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹324 (b) ₹180 (c) ₹36 (d) ₹252
30. 30.If 5 kites cost ₹30, how much do 9 kites cost? (a) ₹34 (b) ₹54 (c) ₹270 (d) ₹60
31. 31.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹215 (b) ₹172 (c) ₹129 (d) ₹43
32. 32.If 8 notebooks cost ₹104, how much do 12 notebooks cost? (a) ₹108 (b) ₹169 (c) ₹156 (d) ₹1248
33. 33.If 9 kites cost ₹72, how much do 2 kites cost? (a) ₹144 (b) ₹65 (c) ₹16 (d) ₹24
34. 34.If 9 pens cost ₹180, how much do 10 pens cost? (a) ₹220 (b) ₹200 (c) ₹181 (d) ₹1800
35. 35.If 2 mangoes cost ₹50, how much do 7 mangoes cost? (a) ₹55 (b) ₹350 (c) ₹175 (d) ₹200
36. 36.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 11 days (c) 12 days (d) 13 days
37. 37.If 9 kites cost ₹162, how much do 11 kites cost? (a) ₹198 (b) ₹164 (c) ₹216 (d) ₹1782
38. 38.If 5 mangoes cost ₹125, how much do 4 mangoes cost? (a) ₹125 (b) ₹100 (c) ₹124 (d) ₹500
39. 39.₹322 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹161 (b) ₹322 (c) ₹46 (d) ₹276
40. 40.If 3 pens cost ₹21, how much do 8 pens cost? (a) ₹26 (b) ₹63 (c) ₹168 (d) ₹56

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad