Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 679 · 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. 1.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 37 days (c) 36 days (d) 15 days
2. 2.If 6 mangoes cost ₹54, how much do 7 mangoes cost? (a) ₹378 (b) ₹72 (c) ₹55 (d) ₹63
3. 3.₹143 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹65 (b) ₹78 (c) ₹13 (d) ₹91
4. 4.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 3 days (d) 11 days
5. 5.If 2 pens cost ₹48, how much do 7 pens cost? (a) ₹192 (b) ₹168 (c) ₹53 (d) ₹336
6. 6.₹462 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹231 (b) ₹336 (c) ₹126 (d) ₹42
7. 7.₹546 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹378 (b) ₹42 (c) ₹273 (d) ₹168
8. 8.₹308 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹22 (b) ₹198 (c) ₹154 (d) ₹110
9. 9.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 14 days (d) 18 days
10. 10.If 6 pens cost ₹42, how much do 9 pens cost? (a) ₹70 (b) ₹63 (c) ₹45 (d) ₹378
11. 11.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 22 days (c) 1 day (d) 21 days
12. 12.If 9 kites cost ₹117, how much do 2 kites cost? (a) ₹110 (b) ₹39 (c) ₹234 (d) ₹26
13. 13.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 2 days (d) 3 days
14. 14.If 6 notebooks cost ₹60, how much do 4 notebooks cost? (a) ₹58 (b) ₹50 (c) ₹240 (d) ₹40
15. 15.If 3 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹24 (b) ₹14 (c) ₹60 (d) ₹20
16. 16.₹192 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹192 (b) ₹48 (c) ₹96 (d) ₹144
17. 17.If 3 mangoes cost ₹75, how much do 5 mangoes cost? (a) ₹375 (b) ₹125 (c) ₹150 (d) ₹77
18. 18.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 8 days (d) 11 days
19. 19.If 5 pens cost ₹30, how much do 8 pens cost? (a) ₹48 (b) ₹240 (c) ₹33 (d) ₹54
20. 20.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 45 days (c) 5 days (d) 9 days
21. 21.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹112 (b) ₹126 (c) ₹63 (d) ₹14
22. 22.₹390 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹30 (b) ₹195 (c) ₹150 (d) ₹240
23. 23.If 2 mangoes cost ₹22, how much do 12 mangoes cost? (a) ₹32 (b) ₹143 (c) ₹264 (d) ₹132
24. 24.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹96 (b) ₹48 (c) ₹80 (d) ₹16
25. 25.5 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 31 days (b) 9 days (c) 30 days (d) 15 days
26. 26.If 8 pens cost ₹32, how much do 2 pens cost? (a) ₹12 (b) ₹64 (c) ₹8 (d) ₹26
27. 27.If 2 notebooks cost ₹6, how much do 11 notebooks cost? (a) ₹15 (b) ₹36 (c) ₹33 (d) ₹66
28. 28.8 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 20 days (c) 40 days (d) 41 days
29. 29.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 14 days (c) 10 days (d) 15 days
30. 30.₹128 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹80 (b) ₹16 (c) ₹64 (d) ₹48
31. 31.₹528 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹48 (b) ₹264 (c) ₹96 (d) ₹432
32. 32.If 3 kites cost ₹72, how much do 2 kites cost? (a) ₹71 (b) ₹72 (c) ₹144 (d) ₹48
33. 33.₹192 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹96 (b) ₹24 (c) ₹72 (d) ₹120
34. 34.If 3 notebooks cost ₹69, how much do 4 notebooks cost? (a) ₹115 (b) ₹70 (c) ₹92 (d) ₹276
35. 35.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 36 days (d) 6 days
36. 36.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 17 days (b) 7 days (c) 11 days (d) 28 days
37. 37.₹350 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹175 (b) ₹350 (c) ₹315 (d) ₹35
38. 38.If 2 mangoes cost ₹26, how much do 3 mangoes cost? (a) ₹78 (b) ₹27 (c) ₹52 (d) ₹39
39. 39.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 6 days (d) 18 days
40. 40.If 2 notebooks cost ₹34, how much do 3 notebooks cost? (a) ₹35 (b) ₹102 (c) ₹51 (d) ₹68

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