Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 380 · 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. 1.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 10 days (c) 16 days (d) 11 days
2. 2.₹220 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹66 (b) ₹154 (c) ₹110 (d) ₹22
3. 3.If 5 notebooks cost ₹80, how much do 8 notebooks cost? (a) ₹144 (b) ₹128 (c) ₹83 (d) ₹640
4. 4.If 6 pens cost ₹150, how much do 2 pens cost? (a) ₹75 (b) ₹50 (c) ₹146 (d) ₹300
5. 5.If 6 notebooks cost ₹48, how much do 7 notebooks cost? (a) ₹336 (b) ₹56 (c) ₹49 (d) ₹64
6. 6.₹350 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹175 (b) ₹350 (c) ₹35 (d) ₹315
7. 7.If 7 notebooks cost ₹119, how much do 11 notebooks cost? (a) ₹123 (b) ₹204 (c) ₹1309 (d) ₹187
8. 8.₹154 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹132 (b) ₹22 (c) ₹154 (d) ₹77
9. 9.₹528 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹48 (b) ₹264 (c) ₹192 (d) ₹336
10. 10.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹99 (b) ₹77 (c) ₹11 (d) ₹55
11. 11.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 14 days (d) 5 days
12. 12.If 5 notebooks cost ₹85, how much do 7 notebooks cost? (a) ₹136 (b) ₹119 (c) ₹87 (d) ₹595
13. 13.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 4 days (d) 49 days
14. 14.If 4 kites cost ₹88, how much do 10 kites cost? (a) ₹94 (b) ₹242 (c) ₹220 (d) ₹880
15. 15.₹72 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹64 (b) ₹72 (c) ₹36 (d) ₹8
16. 16.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 4 days (d) 3 days
17. 17.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 12 days (c) 24 days (d) 25 days
18. 18.If 5 notebooks cost ₹95, how much do 6 notebooks cost? (a) ₹114 (b) ₹133 (c) ₹570 (d) ₹96
19. 19.If 7 notebooks cost ₹77, how much do 12 notebooks cost? (a) ₹132 (b) ₹82 (c) ₹924 (d) ₹143
20. 20.If 5 kites cost ₹80, how much do 7 kites cost? (a) ₹128 (b) ₹112 (c) ₹82 (d) ₹560
21. 21.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹100 (b) ₹50 (c) ₹175 (d) ₹250
22. 22.₹198 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹99 (b) ₹18 (c) ₹90 (d) ₹108
23. 23.3 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) 2 days (d) 3 days
24. 24.If 4 mangoes cost ₹12, how much do 5 mangoes cost? (a) ₹13 (b) ₹18 (c) ₹60 (d) ₹15
25. 25.If 8 pens cost ₹72, how much do 5 pens cost? (a) ₹45 (b) ₹69 (c) ₹360 (d) ₹54
26. 26.If 2 pens cost ₹50, how much do 7 pens cost? (a) ₹55 (b) ₹350 (c) ₹200 (d) ₹175
27. 27.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹44 (b) ₹110 (c) ₹11 (d) ₹99
28. 28.If 2 pens cost ₹48, how much do 3 pens cost? (a) ₹96 (b) ₹144 (c) ₹49 (d) ₹72
29. 29.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 4 days (d) 3 days
30. 30.If 5 kites cost ₹30, how much do 10 kites cost? (a) ₹66 (b) ₹35 (c) ₹60 (d) ₹300
31. 31.₹245 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹35 (b) ₹245 (c) ₹210 (d) ₹211
32. 32.If 2 kites cost ₹28, how much do 4 kites cost? (a) ₹112 (b) ₹30 (c) ₹56 (d) ₹70
33. 33.If 7 notebooks cost ₹147, how much do 9 notebooks cost? (a) ₹1323 (b) ₹149 (c) ₹210 (d) ₹189
34. 34.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 13 days (d) 16 days
35. 35.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹240 (b) ₹432 (c) ₹48 (d) ₹336
36. 36.6 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 12 days (c) 13 days (d) 3 days
37. 37.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 6 days (d) 7 days
38. 38.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 6 days
39. 39.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 13 days (d) 1 day
40. 40.If 9 mangoes cost ₹72, how much do 3 mangoes cost? (a) ₹216 (b) ₹66 (c) ₹24 (d) ₹32

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