Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 454 · 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.₹306 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹34 (b) ₹238 (c) ₹153 (d) ₹68
2. 2.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 13 days (c) 22 days (d) 21 days
3. 3.₹450 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹225 (b) ₹405 (c) ₹450 (d) ₹45
4. 4.₹301 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹86 (b) ₹43 (c) ₹258 (d) ₹215
5. 5.If 7 mangoes cost ₹154, how much do 9 mangoes cost? (a) ₹156 (b) ₹1386 (c) ₹220 (d) ₹198
6. 6.If 5 pens cost ₹95, how much do 4 pens cost? (a) ₹380 (b) ₹94 (c) ₹76 (d) ₹95
7. 7.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 17 days (d) 25 days
8. 8.3 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 21 days (b) 48 days (c) 4 days (d) 3 days
9. 9.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹231 (b) ₹198 (c) ₹33 (d) ₹165
10. 10.If 3 pens cost ₹54, how much do 2 pens cost? (a) ₹53 (b) ₹36 (c) ₹54 (d) ₹108
11. 11.If 8 kites cost ₹160, how much do 3 kites cost? (a) ₹155 (b) ₹80 (c) ₹480 (d) ₹60
12. 12.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 16 days (d) 10 days
13. 13.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 1 day (d) 8 days
14. 14.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹72 (b) ₹9 (c) ₹63 (d) ₹36
15. 15.If 4 notebooks cost ₹68, how much do 5 notebooks cost? (a) ₹69 (b) ₹102 (c) ₹340 (d) ₹85
16. 16.₹240 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹168 (b) ₹120 (c) ₹24 (d) ₹72
17. 17.If 3 pens cost ₹75, how much do 8 pens cost? (a) ₹600 (b) ₹225 (c) ₹200 (d) ₹80
18. 18.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹18 (c) ₹36 (d) ₹24
19. 19.If 4 pens cost ₹28, how much do 5 pens cost? (a) ₹35 (b) ₹140 (c) ₹29 (d) ₹42
20. 20.If 2 pens cost ₹42, how much do 10 pens cost? (a) ₹420 (b) ₹50 (c) ₹210 (d) ₹231
21. 21.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 22 days (c) 23 days (d) 7 days
22. 22.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 25 days (b) 13 days (c) 17 days (d) 9 days
23. 23.If 7 kites cost ₹84, how much do 2 kites cost? (a) ₹168 (b) ₹79 (c) ₹36 (d) ₹24
24. 24.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹24 (b) ₹72 (c) ₹96 (d) ₹84
25. 25.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 4 days
26. 26.If 2 pens cost ₹28, how much do 4 pens cost? (a) ₹30 (b) ₹56 (c) ₹112 (d) ₹70
27. 27.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 19 days (c) 11 days (d) 45 days
28. 28.If 6 notebooks cost ₹60, how much do 3 notebooks cost? (a) ₹30 (b) ₹180 (c) ₹40 (d) ₹57
29. 29.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 13 days (d) 12 days
30. 30.If 3 mangoes cost ₹60, how much do 9 mangoes cost? (a) ₹66 (b) ₹540 (c) ₹180 (d) ₹200
31. 31.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹6 (b) ₹24 (c) ₹54 (d) ₹39
32. 32.6 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 12 days (d) 11 days
33. 33.If 7 mangoes cost ₹49, how much do 12 mangoes cost? (a) ₹588 (b) ₹54 (c) ₹84 (d) ₹91
34. 34.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹93 (b) ₹31 (c) ₹62 (d) ₹124
35. 35.If 4 notebooks cost ₹88, how much do 2 notebooks cost? (a) ₹44 (b) ₹86 (c) ₹66 (d) ₹176
36. 36.If 4 kites cost ₹16, how much do 5 kites cost? (a) ₹20 (b) ₹24 (c) ₹17 (d) ₹80
37. 37.₹378 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹27 (b) ₹189 (c) ₹243 (d) ₹135
38. 38.If 3 pens cost ₹18, how much do 12 pens cost? (a) ₹78 (b) ₹216 (c) ₹72 (d) ₹27
39. 39.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 34 days (d) 33 days
40. 40.If 5 kites cost ₹25, how much do 4 kites cost? (a) ₹20 (b) ₹24 (c) ₹25 (d) ₹100

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