Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 775 · 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 pens cost ₹72, how much do 3 pens cost? (a) ₹216 (b) ₹24 (c) ₹66 (d) ₹32
2. 2.If 6 notebooks cost ₹42, how much do 12 notebooks cost? (a) ₹91 (b) ₹504 (c) ₹84 (d) ₹48
3. 3.5 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
4. 4.If 7 kites cost ₹147, how much do 8 kites cost? (a) ₹189 (b) ₹1176 (c) ₹148 (d) ₹168
5. 5.If 5 mangoes cost ₹115, how much do 6 mangoes cost? (a) ₹161 (b) ₹116 (c) ₹138 (d) ₹690
6. 6.If 2 notebooks cost ₹46, how much do 10 notebooks cost? (a) ₹54 (b) ₹460 (c) ₹230 (d) ₹253
7. 7.If 5 mangoes cost ₹120, how much do 12 mangoes cost? (a) ₹1440 (b) ₹127 (c) ₹288 (d) ₹312
8. 8.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹36 (b) ₹108 (c) ₹90 (d) ₹72
9. 9.If 4 notebooks cost ₹88, how much do 7 notebooks cost? (a) ₹616 (b) ₹154 (c) ₹91 (d) ₹176
10. 10.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹6 (b) ₹27 (c) ₹30 (d) ₹24
11. 11.If 9 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹20 (b) ₹25 (c) ₹40 (d) ₹180
12. 12.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 4 days (d) 5 days
13. 13.₹176 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹16 (b) ₹80 (c) ₹88 (d) ₹96
14. 14.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 6 days (d) 20 days
15. 15.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 10 days (d) 5 days
16. 16.If 5 pens cost ₹20, how much do 9 pens cost? (a) ₹24 (b) ₹36 (c) ₹40 (d) ₹180
17. 17.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 5 days
18. 18.If 7 mangoes cost ₹56, how much do 2 mangoes cost? (a) ₹24 (b) ₹51 (c) ₹112 (d) ₹16
19. 19.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹225 (b) ₹200 (c) ₹50 (d) ₹250
20. 20.If 5 pens cost ₹35, how much do 4 pens cost? (a) ₹140 (b) ₹34 (c) ₹35 (d) ₹28
21. 21.₹325 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹125 (b) ₹200 (c) ₹225 (d) ₹25
22. 22.If 2 kites cost ₹8, how much do 8 kites cost? (a) ₹36 (b) ₹64 (c) ₹14 (d) ₹32
23. 23.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 8 days (b) 28 days (c) 20 days (d) 7 days
24. 24.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹204 (b) ₹170 (c) ₹187 (d) ₹34
25. 25.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹37 (b) ₹333 (c) ₹296 (d) ₹297
26. 26.If 5 notebooks cost ₹115, how much do 9 notebooks cost? (a) ₹207 (b) ₹119 (c) ₹1035 (d) ₹230
27. 27.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹78 (b) ₹39 (c) ₹156 (d) ₹117
28. 28.₹232 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹116 (b) ₹203 (c) ₹29 (d) ₹232
29. 29.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 14 days (d) 19 days
30. 30.If 3 mangoes cost ₹57, how much do 4 mangoes cost? (a) ₹76 (b) ₹228 (c) ₹58 (d) ₹95
31. 31.5 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 15 days (d) 3 days
32. 32.₹132 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹88 (b) ₹132 (c) ₹66 (d) ₹44
33. 33.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 2 days (d) 6 days
34. 34.₹110 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹99 (b) ₹11 (c) ₹55 (d) ₹110
35. 35.If 2 pens cost ₹14, how much do 10 pens cost? (a) ₹70 (b) ₹22 (c) ₹77 (d) ₹140
36. 36.₹25 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹5 (d) ₹15
37. 37.₹150 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹15 (b) ₹45 (c) ₹75 (d) ₹105
38. 38.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹13 (b) ₹91 (c) ₹26 (d) ₹104
39. 39.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹280 (c) ₹240 (d) ₹40
40. 40.If 8 kites cost ₹96, how much do 3 kites cost? (a) ₹48 (b) ₹36 (c) ₹288 (d) ₹91

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