Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 614 · 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. 1.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 19 days (c) 7 days (d) 18 days
2. 2.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹51 (b) ₹17 (c) ₹153 (d) ₹136
3. 3.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 9 days (d) 2 days
4. 4.If 3 pens cost ₹21, how much do 10 pens cost? (a) ₹77 (b) ₹70 (c) ₹28 (d) ₹210
5. 5.₹55 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹22 (b) ₹11 (c) ₹44 (d) ₹33
6. 6.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 3 days
7. 7.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 14 days (d) 9 days
8. 8.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 1 day (d) 17 days
9. 9.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 5 days (d) 20 days
10. 10.If 8 pens cost ₹168, how much do 3 pens cost? (a) ₹163 (b) ₹84 (c) ₹504 (d) ₹63
11. 11.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹14 (b) ₹21 (c) ₹7 (d) ₹28
12. 12.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 3 days
13. 13.If 8 mangoes cost ₹48, how much do 10 mangoes cost? (a) ₹66 (b) ₹50 (c) ₹480 (d) ₹60
14. 14.If 5 kites cost ₹80, how much do 12 kites cost? (a) ₹208 (b) ₹960 (c) ₹192 (d) ₹87
15. 15.If 6 mangoes cost ₹60, how much do 8 mangoes cost? (a) ₹62 (b) ₹480 (c) ₹90 (d) ₹80
16. 16.If 8 pens cost ₹200, how much do 9 pens cost? (a) ₹250 (b) ₹1800 (c) ₹225 (d) ₹201
17. 17.8 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 25 days (c) 24 days (d) 4 days
18. 18.If 2 kites cost ₹38, how much do 9 kites cost? (a) ₹45 (b) ₹342 (c) ₹171 (d) ₹190
19. 19.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 14 days (d) 5 days
20. 20.If 9 pens cost ₹63, how much do 4 pens cost? (a) ₹252 (b) ₹28 (c) ₹58 (d) ₹35
21. 21.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 7 days (d) 11 days
22. 22.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 5 days (d) 9 days
23. 23.₹396 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹108 (b) ₹288 (c) ₹36 (d) ₹198
24. 24.If 8 notebooks cost ₹32, how much do 7 notebooks cost? (a) ₹28 (b) ₹32 (c) ₹224 (d) ₹31
25. 25.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 10 days (d) 17 days
26. 26.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹70 (b) ₹10 (c) ₹60 (d) ₹50
27. 27.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹119 (d) ₹136
28. 28.If 2 mangoes cost ₹40, how much do 3 mangoes cost? (a) ₹41 (b) ₹60 (c) ₹120 (d) ₹80
29. 29.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 33 days (d) 32 days
30. 30.9 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 31 days (c) 30 days (d) 16 days
31. 31.If 5 pens cost ₹95, how much do 11 pens cost? (a) ₹1045 (b) ₹101 (c) ₹209 (d) ₹228
32. 32.If 3 kites cost ₹75, how much do 7 kites cost? (a) ₹79 (b) ₹175 (c) ₹200 (d) ₹525
33. 33.If 6 kites cost ₹138, how much do 4 kites cost? (a) ₹552 (b) ₹136 (c) ₹115 (d) ₹92
34. 34.If 6 pens cost ₹30, how much do 3 pens cost? (a) ₹15 (b) ₹90 (c) ₹27 (d) ₹20
35. 35.₹301 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹172 (b) ₹215 (c) ₹43 (d) ₹129
36. 36.₹650 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹325 (b) ₹400 (c) ₹250 (d) ₹50
37. 37.₹343 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹295 (b) ₹343 (c) ₹49 (d) ₹294
38. 38.If 3 pens cost ₹39, how much do 10 pens cost? (a) ₹46 (b) ₹143 (c) ₹390 (d) ₹130
39. 39.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 16 days (c) 9 days (d) 15 days
40. 40.₹65 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹52 (b) ₹53 (c) ₹65 (d) ₹13

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