Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 370 · 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 5 mangoes cost ₹35, how much do 10 mangoes cost? (a) ₹40 (b) ₹77 (c) ₹70 (d) ₹350
2. 2.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 12 days (c) 14 days (d) 13 days
3. 3.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 10 days (d) 8 days
4. 4.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹46 (b) ₹230 (c) ₹322 (d) ₹276
5. 5.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 8 days (d) 6 days
6. 6.If 5 notebooks cost ₹75, how much do 3 notebooks cost? (a) ₹225 (b) ₹60 (c) ₹73 (d) ₹45
7. 7.₹180 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹45 (b) ₹180 (c) ₹135 (d) ₹90
8. 8.₹88 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹16 (b) ₹8 (c) ₹72 (d) ₹44
9. 9.₹300 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹300 (b) ₹150 (c) ₹250 (d) ₹50
10. 10.₹462 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹84 (b) ₹42 (c) ₹231 (d) ₹378
11. 11.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 34 days (b) 7 days (c) 15 days (d) 33 days
12. 12.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹216 (b) ₹96 (c) ₹156 (d) ₹24
13. 13.If 3 notebooks cost ₹51, how much do 7 notebooks cost? (a) ₹357 (b) ₹119 (c) ₹55 (d) ₹136
14. 14.If 3 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹240 (b) ₹80 (c) ₹88 (d) ₹31
15. 15.If 2 mangoes cost ₹42, how much do 3 mangoes cost? (a) ₹63 (b) ₹43 (c) ₹126 (d) ₹84
16. 16.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹36 (b) ₹24 (c) ₹12 (d) ₹48
17. 17.If 7 kites cost ₹56, how much do 12 kites cost? (a) ₹96 (b) ₹104 (c) ₹61 (d) ₹672
18. 18.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹7 (b) ₹28 (c) ₹49 (d) ₹56
19. 19.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 19 days (d) 4 days
20. 20.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹286 (b) ₹44 (c) ₹352 (d) ₹220
21. 21.If 4 kites cost ₹88, how much do 3 kites cost? (a) ₹66 (b) ₹88 (c) ₹87 (d) ₹264
22. 22.₹195 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹150 (b) ₹15 (c) ₹135 (d) ₹60
23. 23.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹14 (b) ₹112 (c) ₹126 (d) ₹63
24. 24.If 3 notebooks cost ₹72, how much do 5 notebooks cost? (a) ₹360 (b) ₹144 (c) ₹120 (d) ₹74
25. 25.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹93 (b) ₹115 (c) ₹92 (d) ₹23
26. 26.₹400 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹200 (d) ₹150
27. 27.If 5 pens cost ₹125, how much do 8 pens cost? (a) ₹1000 (b) ₹225 (c) ₹200 (d) ₹128
28. 28.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 12 days (d) 8 days
29. 29.₹215 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹215 (b) ₹172 (c) ₹173 (d) ₹43
30. 30.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 17 days (c) 32 days (d) 33 days
31. 31.₹200 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹80 (b) ₹120 (c) ₹100 (d) ₹40
32. 32.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 13 days (c) 5 days (d) 11 days
33. 33.If 4 pens cost ₹80, how much do 11 pens cost? (a) ₹880 (b) ₹87 (c) ₹240 (d) ₹220
34. 34.₹130 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹130 (b) ₹65 (c) ₹26 (d) ₹104
35. 35.If 7 kites cost ₹63, how much do 2 kites cost? (a) ₹18 (b) ₹27 (c) ₹58 (d) ₹126
36. 36.₹238 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹34 (b) ₹119 (c) ₹170 (d) ₹68
37. 37.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 11 days
38. 38.If 4 mangoes cost ₹72, how much do 2 mangoes cost? (a) ₹144 (b) ₹70 (c) ₹36 (d) ₹54
39. 39.8 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 40 days (c) 4 days (d) 41 days
40. 40.If 5 pens cost ₹125, how much do 2 pens cost? (a) ₹50 (b) ₹122 (c) ₹250 (d) ₹75

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