Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 302 · 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 3 notebooks cost ₹72, how much do 10 notebooks cost? (a) ₹264 (b) ₹79 (c) ₹720 (d) ₹240
2. 2.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 3 days (d) 4 days
3. 3.₹130 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹65 (b) ₹117 (c) ₹13 (d) ₹130
4. 4.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 9 days (c) 15 days (d) 1 day
5. 5.If 4 notebooks cost ₹68, how much do 5 notebooks cost? (a) ₹102 (b) ₹340 (c) ₹69 (d) ₹85
6. 6.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 7 days (d) 23 days
7. 7.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹324 (b) ₹162 (c) ₹36 (d) ₹288
8. 8.If 2 pens cost ₹22, how much do 10 pens cost? (a) ₹110 (b) ₹30 (c) ₹220 (d) ₹121
9. 9.If 3 notebooks cost ₹66, how much do 10 notebooks cost? (a) ₹242 (b) ₹660 (c) ₹220 (d) ₹73
10. 10.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 13 days (d) 8 days
11. 11.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 36 days (c) 35 days (d) 5 days
12. 12.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹35 (b) ₹40 (c) ₹5 (d) ₹20
13. 13.If 5 notebooks cost ₹55, how much do 7 notebooks cost? (a) ₹385 (b) ₹88 (c) ₹57 (d) ₹77
14. 14.8 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 12 days (b) 25 days (c) 18 days (d) 24 days
15. 15.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 40 days (d) 39 days
16. 16.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹200 (b) ₹275 (c) ₹350 (d) ₹50
17. 17.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 11 days (c) 15 days (d) 16 days
18. 18.If 9 mangoes cost ₹207, how much do 7 mangoes cost? (a) ₹184 (b) ₹161 (c) ₹205 (d) ₹1449
19. 19.If 9 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹31 (b) ₹144 (c) ₹20 (d) ₹16
20. 20.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 56 days (b) 8 days (c) 57 days (d) 20 days
21. 21.If 5 pens cost ₹20, how much do 9 pens cost? (a) ₹24 (b) ₹180 (c) ₹40 (d) ₹36
22. 22.If 7 kites cost ₹70, how much do 2 kites cost? (a) ₹30 (b) ₹140 (c) ₹65 (d) ₹20
23. 23.If 4 mangoes cost ₹32, how much do 8 mangoes cost? (a) ₹256 (b) ₹72 (c) ₹36 (d) ₹64
24. 24.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 9 days (c) 22 days (d) 15 days
25. 25.₹520 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹40 (b) ₹260 (c) ₹360 (d) ₹160
26. 26.If 6 notebooks cost ₹78, how much do 2 notebooks cost? (a) ₹26 (b) ₹39 (c) ₹156 (d) ₹74
27. 27.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹55 (b) ₹10 (c) ₹60 (d) ₹50
28. 28.If 4 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹240 (b) ₹30 (c) ₹60 (d) ₹66
29. 29.If 4 mangoes cost ₹88, how much do 8 mangoes cost? (a) ₹198 (b) ₹704 (c) ₹92 (d) ₹176
30. 30.If 5 mangoes cost ₹100, how much do 3 mangoes cost? (a) ₹80 (b) ₹300 (c) ₹98 (d) ₹60
31. 31.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 17 days (c) 16 days (d) 10 days
32. 32.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 12 days (d) 5 days
33. 33.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹240 (b) ₹200 (c) ₹280 (d) ₹40
34. 34.If 4 kites cost ₹20, how much do 3 kites cost? (a) ₹19 (b) ₹60 (c) ₹20 (d) ₹15
35. 35.If 3 pens cost ₹9, how much do 10 pens cost? (a) ₹30 (b) ₹33 (c) ₹90 (d) ₹16
36. 36.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 6 days (d) 16 days
37. 37.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 17 days (d) 11 days
38. 38.If 2 pens cost ₹46, how much do 6 pens cost? (a) ₹276 (b) ₹161 (c) ₹50 (d) ₹138
39. 39.₹180 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹72 (b) ₹90 (c) ₹108 (d) ₹36
40. 40.If 7 mangoes cost ₹63, how much do 4 mangoes cost? (a) ₹60 (b) ₹45 (c) ₹252 (d) ₹36

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