Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 961 · 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.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹56 (b) ₹28 (c) ₹7 (d) ₹49
2. 2.4 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 13 days (d) 16 days
3. 3.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹22 (b) ₹176 (c) ₹66 (d) ₹121
4. 4.If 9 mangoes cost ₹144, how much do 5 mangoes cost? (a) ₹96 (b) ₹720 (c) ₹140 (d) ₹80
5. 5.₹330 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹330 (b) ₹165 (c) ₹33 (d) ₹297
6. 6.₹160 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹128 (b) ₹80 (c) ₹32 (d) ₹160
7. 7.If 7 notebooks cost ₹63, how much do 12 notebooks cost? (a) ₹117 (b) ₹756 (c) ₹108 (d) ₹68
8. 8.₹192 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹144 (b) ₹192 (c) ₹96 (d) ₹48
9. 9.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 6 days (d) 4 days
10. 10.₹160 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹80 (b) ₹144 (c) ₹160 (d) ₹16
11. 11.If 4 pens cost ₹20, how much do 2 pens cost? (a) ₹10 (b) ₹18 (c) ₹40 (d) ₹15
12. 12.If 5 mangoes cost ₹90, how much do 6 mangoes cost? (a) ₹126 (b) ₹108 (c) ₹91 (d) ₹540
13. 13.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 8 days (c) 5 days (d) 20 days
14. 14.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹250 (b) ₹225 (c) ₹200 (d) ₹50
15. 15.If 8 mangoes cost ₹120, how much do 11 mangoes cost? (a) ₹123 (b) ₹1320 (c) ₹180 (d) ₹165
16. 16.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 14 days (c) 2 days (d) 3 days
17. 17.₹121 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹77 (b) ₹11 (c) ₹88 (d) ₹44
18. 18.If 5 pens cost ₹60, how much do 7 pens cost? (a) ₹420 (b) ₹84 (c) ₹62 (d) ₹96
19. 19.If 2 mangoes cost ₹32, how much do 9 mangoes cost? (a) ₹39 (b) ₹160 (c) ₹144 (d) ₹288
20. 20.₹70 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹35 (b) ₹30 (c) ₹40 (d) ₹10
21. 21.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 11 days (d) 10 days
22. 22.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 53 days (b) 19 days (c) 7 days (d) 52 days
23. 23.₹120 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹60 (b) ₹24 (c) ₹72 (d) ₹48
24. 24.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 3 days (c) 10 days (d) 7 days
25. 25.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 1 day (c) 15 days (d) 16 days
26. 26.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹108 (b) ₹36 (c) ₹180 (d) ₹144
27. 27.₹132 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹110 (b) ₹132 (c) ₹22 (d) ₹66
28. 28.If 7 pens cost ₹98, how much do 4 pens cost? (a) ₹70 (b) ₹95 (c) ₹392 (d) ₹56
29. 29.If 8 notebooks cost ₹200, how much do 3 notebooks cost? (a) ₹75 (b) ₹600 (c) ₹100 (d) ₹195
30. 30.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 5 days (d) 14 days
31. 31.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 5 days (d) 7 days
32. 32.If 2 notebooks cost ₹44, how much do 6 notebooks cost? (a) ₹264 (b) ₹48 (c) ₹132 (d) ₹154
33. 33.If 2 pens cost ₹10, how much do 7 pens cost? (a) ₹15 (b) ₹40 (c) ₹70 (d) ₹35
34. 34.If 9 pens cost ₹99, how much do 10 pens cost? (a) ₹990 (b) ₹121 (c) ₹100 (d) ₹110
35. 35.₹175 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹125 (b) ₹50 (c) ₹25 (d) ₹150
36. 36.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 9 days (d) 4 days
37. 37.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 49 days (c) 9 days (d) 4 days
38. 38.If 3 pens cost ₹21, how much do 4 pens cost? (a) ₹22 (b) ₹28 (c) ₹84 (d) ₹35
39. 39.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 11 days (c) 26 days (d) 27 days
40. 40.₹234 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹117 (b) ₹52 (c) ₹182 (d) ₹26

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