Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 393 · 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.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹405 (b) ₹45 (c) ₹225 (d) ₹315
2. 2.4 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) 22 days (d) 23 days
3. 3.If 7 pens cost ₹70, how much do 5 pens cost? (a) ₹350 (b) ₹50 (c) ₹60 (d) ₹68
4. 4.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 44 days (c) 45 days (d) 17 days
5. 5.If 8 pens cost ₹160, how much do 7 pens cost? (a) ₹160 (b) ₹140 (c) ₹159 (d) ₹1120
6. 6.₹36 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹27 (b) ₹36 (c) ₹9 (d) ₹18
7. 7.If 4 kites cost ₹32, how much do 8 kites cost? (a) ₹256 (b) ₹72 (c) ₹36 (d) ₹64
8. 8.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹11 (b) ₹44 (c) ₹55 (d) ₹66
9. 9.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
10. 10.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 14 days (c) 18 days (d) 2 days
11. 11.₹144 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹144 (b) ₹16 (c) ₹128 (d) ₹72
12. 12.If 8 pens cost ₹176, how much do 3 pens cost? (a) ₹528 (b) ₹171 (c) ₹66 (d) ₹88
13. 13.If 4 mangoes cost ₹16, how much do 11 mangoes cost? (a) ₹176 (b) ₹23 (c) ₹48 (d) ₹44
14. 14.If 6 kites cost ₹60, how much do 11 kites cost? (a) ₹660 (b) ₹65 (c) ₹120 (d) ₹110
15. 15.₹440 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹360 (b) ₹220 (c) ₹80 (d) ₹40
16. 16.₹261 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹233 (b) ₹261 (c) ₹232 (d) ₹29
17. 17.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹30 (b) ₹33 (c) ₹6 (d) ₹36
18. 18.₹429 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹195 (b) ₹273 (c) ₹234 (d) ₹39
19. 19.If 9 pens cost ₹216, how much do 10 pens cost? (a) ₹264 (b) ₹217 (c) ₹2160 (d) ₹240
20. 20.If 4 pens cost ₹68, how much do 10 pens cost? (a) ₹680 (b) ₹187 (c) ₹170 (d) ₹74
21. 21.If 7 notebooks cost ₹63, how much do 11 notebooks cost? (a) ₹67 (b) ₹693 (c) ₹99 (d) ₹108
22. 22.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹16 (b) ₹20 (c) ₹24 (d) ₹8
23. 23.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 26 days (c) 27 days (d) 16 days
24. 24.If 2 pens cost ₹32, how much do 5 pens cost? (a) ₹80 (b) ₹160 (c) ₹96 (d) ₹35
25. 25.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 16 days (d) 7 days
26. 26.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹275 (b) ₹300 (c) ₹250 (d) ₹50
27. 27.4 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 27 days (b) 1 day (c) 17 days (d) 3 days
28. 28.If 5 notebooks cost ₹20, how much do 3 notebooks cost? (a) ₹60 (b) ₹18 (c) ₹16 (d) ₹12
29. 29.If 3 kites cost ₹27, how much do 9 kites cost? (a) ₹243 (b) ₹33 (c) ₹90 (d) ₹81
30. 30.If 2 notebooks cost ₹40, how much do 7 notebooks cost? (a) ₹45 (b) ₹140 (c) ₹280 (d) ₹160
31. 31.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 49 days (c) 19 days (d) 4 days
32. 32.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 31 days (c) 15 days (d) 30 days
33. 33.If 9 pens cost ₹81, how much do 6 pens cost? (a) ₹54 (b) ₹78 (c) ₹486 (d) ₹63
34. 34.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 8 days (d) 7 days
35. 35.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹168 (b) ₹132 (c) ₹24 (d) ₹96
36. 36.If 3 kites cost ₹9, how much do 7 kites cost? (a) ₹63 (b) ₹13 (c) ₹24 (d) ₹21
37. 37.₹198 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹22 (b) ₹154 (c) ₹99 (d) ₹44
38. 38.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 17 days (d) 7 days
39. 39.If 5 kites cost ₹75, how much do 4 kites cost? (a) ₹75 (b) ₹60 (c) ₹300 (d) ₹74
40. 40.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 18 days (c) 6 days (d) 48 days

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