Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 965 · 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 7 notebooks cost ₹42, how much do 5 notebooks cost? (a) ₹30 (b) ₹36 (c) ₹210 (d) ₹40
2. 2.If 9 notebooks cost ₹72, how much do 12 notebooks cost? (a) ₹104 (b) ₹864 (c) ₹75 (d) ₹96
3. 3.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 1 day (d) 10 days
4. 4.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹78 (b) ₹26 (c) ₹130 (d) ₹104
5. 5.₹231 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹199 (b) ₹33 (c) ₹198 (d) ₹231
6. 6.₹297 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹189 (b) ₹27 (c) ₹135 (d) ₹162
7. 7.6 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 10 days (c) 14 days (d) 9 days
8. 8.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 1 day (c) 16 days (d) 9 days
9. 9.If 5 kites cost ₹100, how much do 2 kites cost? (a) ₹60 (b) ₹40 (c) ₹97 (d) ₹200
10. 10.₹494 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹304 (b) ₹247 (c) ₹38 (d) ₹190
11. 11.If 5 notebooks cost ₹85, how much do 7 notebooks cost? (a) ₹119 (b) ₹87 (c) ₹136 (d) ₹595
12. 12.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 9 days (d) 49 days
13. 13.If 2 kites cost ₹44, how much do 6 kites cost? (a) ₹154 (b) ₹264 (c) ₹132 (d) ₹48
14. 14.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹90 (b) ₹63 (c) ₹36 (d) ₹18
15. 15.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 14 days (d) 15 days
16. 16.If 3 mangoes cost ₹51, how much do 4 mangoes cost? (a) ₹85 (b) ₹52 (c) ₹68 (d) ₹204
17. 17.If 6 pens cost ₹24, how much do 7 pens cost? (a) ₹28 (b) ₹168 (c) ₹32 (d) ₹25
18. 18.If 6 notebooks cost ₹120, how much do 4 notebooks cost? (a) ₹118 (b) ₹80 (c) ₹480 (d) ₹100
19. 19.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 16 days (b) 13 days (c) 12 days (d) 14 days
20. 20.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 3 days (d) 8 days
21. 21.₹572 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹286 (b) ₹176 (c) ₹44 (d) ₹396
22. 22.If 8 kites cost ₹128, how much do 3 kites cost? (a) ₹48 (b) ₹64 (c) ₹384 (d) ₹123
23. 23.₹66 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹6 (b) ₹18 (c) ₹33 (d) ₹48
24. 24.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 6 days
25. 25.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 7 days (d) 8 days
26. 26.If 5 pens cost ₹20, how much do 4 pens cost? (a) ₹19 (b) ₹80 (c) ₹16 (d) ₹20
27. 27.If 4 pens cost ₹88, how much do 7 pens cost? (a) ₹616 (b) ₹91 (c) ₹154 (d) ₹176
28. 28.If 7 notebooks cost ₹112, how much do 10 notebooks cost? (a) ₹176 (b) ₹1120 (c) ₹115 (d) ₹160
29. 29.If 5 pens cost ₹110, how much do 6 pens cost? (a) ₹154 (b) ₹111 (c) ₹660 (d) ₹132
30. 30.₹330 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹270 (b) ₹165 (c) ₹30 (d) ₹60
31. 31.If 2 mangoes cost ₹48, how much do 9 mangoes cost? (a) ₹55 (b) ₹432 (c) ₹240 (d) ₹216
32. 32.If 9 kites cost ₹144, how much do 10 kites cost? (a) ₹176 (b) ₹160 (c) ₹145 (d) ₹1440
33. 33.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 23 days (b) 15 days (c) 7 days (d) 22 days
34. 34.If 3 notebooks cost ₹36, how much do 12 notebooks cost? (a) ₹45 (b) ₹156 (c) ₹144 (d) ₹432
35. 35.₹336 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹48 (b) ₹168 (c) ₹288 (d) ₹336
36. 36.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 4 days (c) 3 days (d) 2 days
37. 37.7 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 11 days (d) 14 days
38. 38.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 15 days (d) 11 days
39. 39.If 2 pens cost ₹36, how much do 8 pens cost? (a) ₹144 (b) ₹42 (c) ₹162 (d) ₹288
40. 40.₹39 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹39 (d) ₹27

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