Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 562 · 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.If 9 kites cost ₹216, how much do 10 kites cost? (a) ₹240 (b) ₹264 (c) ₹2160 (d) ₹217
2. 2.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 20 days (c) 11 days (d) 21 days
3. 3.₹300 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹90 (b) ₹30 (c) ₹210 (d) ₹150
4. 4.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹78 (b) ₹117 (c) ₹156 (d) ₹39
5. 5.₹280 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹160 (b) ₹140 (c) ₹120 (d) ₹40
6. 6.If 5 notebooks cost ₹80, how much do 12 notebooks cost? (a) ₹960 (b) ₹87 (c) ₹192 (d) ₹208
7. 7.If 4 mangoes cost ₹68, how much do 3 mangoes cost? (a) ₹67 (b) ₹51 (c) ₹204 (d) ₹68
8. 8.₹190 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹190 (b) ₹19 (c) ₹95 (d) ₹171
9. 9.If 5 notebooks cost ₹125, how much do 10 notebooks cost? (a) ₹250 (b) ₹275 (c) ₹1250 (d) ₹130
10. 10.If 3 kites cost ₹15, how much do 4 kites cost? (a) ₹16 (b) ₹25 (c) ₹60 (d) ₹20
11. 11.If 4 mangoes cost ₹16, how much do 10 mangoes cost? (a) ₹40 (b) ₹160 (c) ₹22 (d) ₹44
12. 12.₹72 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹36 (b) ₹56 (c) ₹8 (d) ₹16
13. 13.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹100 (b) ₹125 (c) ₹25 (d) ₹150
14. 14.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹108 (b) ₹27 (c) ₹54 (d) ₹81
15. 15.If 5 mangoes cost ₹60, how much do 11 mangoes cost? (a) ₹144 (b) ₹132 (c) ₹660 (d) ₹66
16. 16.If 2 notebooks cost ₹26, how much do 4 notebooks cost? (a) ₹28 (b) ₹104 (c) ₹65 (d) ₹52
17. 17.₹160 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹140 (b) ₹80 (c) ₹20 (d) ₹160
18. 18.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹14 (b) ₹21 (c) ₹15 (d) ₹7
19. 19.If 5 pens cost ₹85, how much do 3 pens cost? (a) ₹83 (b) ₹51 (c) ₹255 (d) ₹68
20. 20.₹164 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹82 (b) ₹123 (c) ₹164 (d) ₹41
21. 21.If 7 notebooks cost ₹70, how much do 12 notebooks cost? (a) ₹75 (b) ₹840 (c) ₹130 (d) ₹120
22. 22.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹16 (b) ₹104 (c) ₹80 (d) ₹128
23. 23.If 6 notebooks cost ₹24, how much do 7 notebooks cost? (a) ₹25 (b) ₹168 (c) ₹28 (d) ₹32
24. 24.If 2 pens cost ₹30, how much do 10 pens cost? (a) ₹38 (b) ₹165 (c) ₹150 (d) ₹300
25. 25.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 17 days (d) 5 days
26. 26.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 5 days (c) 44 days (d) 45 days
27. 27.If 4 mangoes cost ₹72, how much do 12 mangoes cost? (a) ₹234 (b) ₹216 (c) ₹864 (d) ₹80
28. 28.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 5 days (c) 12 days (d) 4 days
29. 29.If 5 pens cost ₹55, how much do 7 pens cost? (a) ₹77 (b) ₹88 (c) ₹385 (d) ₹57
30. 30.If 2 notebooks cost ₹28, how much do 4 notebooks cost? (a) ₹112 (b) ₹56 (c) ₹70 (d) ₹30
31. 31.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 6 days (d) 5 days
32. 32.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹136 (b) ₹17 (c) ₹153 (d) ₹85
33. 33.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 64 days (b) 21 days (c) 7 days (d) 63 days
34. 34.If 2 notebooks cost ₹28, how much do 9 notebooks cost? (a) ₹252 (b) ₹35 (c) ₹140 (d) ₹126
35. 35.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹140 (b) ₹196 (c) ₹28 (d) ₹168
36. 36.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 10 days (c) 8 days (d) 13 days
37. 37.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 2 days (d) 4 days
38. 38.If 3 pens cost ₹9, how much do 4 pens cost? (a) ₹10 (b) ₹12 (c) ₹36 (d) ₹15
39. 39.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹9 (b) ₹27 (c) ₹63 (d) ₹45
40. 40.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 16 days (d) 12 days

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