Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 407 · 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.₹350 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹105 (b) ₹175 (c) ₹245 (d) ₹35
2. 2.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 5 days (c) 34 days (d) 17 days
3. 3.If 6 pens cost ₹36, how much do 7 pens cost? (a) ₹37 (b) ₹252 (c) ₹48 (d) ₹42
4. 4.₹546 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹210 (b) ₹336 (c) ₹42 (d) ₹273
5. 5.If 9 notebooks cost ₹144, how much do 3 notebooks cost? (a) ₹64 (b) ₹432 (c) ₹138 (d) ₹48
6. 6.If 7 kites cost ₹133, how much do 10 kites cost? (a) ₹209 (b) ₹136 (c) ₹190 (d) ₹1330
7. 7.If 9 mangoes cost ₹216, how much do 12 mangoes cost? (a) ₹2592 (b) ₹288 (c) ₹219 (d) ₹312
8. 8.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 18 days (d) 10 days
9. 9.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 45 days (d) 21 days
10. 10.If 2 pens cost ₹34, how much do 9 pens cost? (a) ₹41 (b) ₹306 (c) ₹170 (d) ₹153
11. 11.If 2 kites cost ₹12, how much do 3 kites cost? (a) ₹18 (b) ₹24 (c) ₹13 (d) ₹36
12. 12.If 4 mangoes cost ₹32, how much do 12 mangoes cost? (a) ₹384 (b) ₹96 (c) ₹40 (d) ₹104
13. 13.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 4 days (c) 5 days (d) 36 days
14. 14.₹460 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹138 (b) ₹46 (c) ₹230 (d) ₹322
15. 15.If 2 pens cost ₹18, how much do 3 pens cost? (a) ₹19 (b) ₹27 (c) ₹36 (d) ₹54
16. 16.If 7 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹16 (b) ₹24 (c) ₹84 (d) ₹12
17. 17.If 5 pens cost ₹70, how much do 12 pens cost? (a) ₹840 (b) ₹77 (c) ₹182 (d) ₹168
18. 18.₹405 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹360 (b) ₹315 (c) ₹90 (d) ₹45
19. 19.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹58 (b) ₹145 (c) ₹174 (d) ₹29
20. 20.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 27 days (d) 3 days
21. 21.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹89 (b) ₹11 (c) ₹99 (d) ₹88
22. 22.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 13 days (c) 27 days (d) 28 days
23. 23.₹288 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹180 (b) ₹108 (c) ₹36 (d) ₹144
24. 24.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹232 (b) ₹29 (c) ₹145 (d) ₹261
25. 25.If 3 kites cost ₹18, how much do 4 kites cost? (a) ₹19 (b) ₹30 (c) ₹24 (d) ₹72
26. 26.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹216 (b) ₹240 (c) ₹48 (d) ₹192
27. 27.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹153 (d) ₹170
28. 28.₹60 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹60 (b) ₹6 (c) ₹30 (d) ₹54
29. 29.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹96 (b) ₹80 (c) ₹112 (d) ₹16
30. 30.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 18 days (d) 11 days
31. 31.If 7 mangoes cost ₹98, how much do 9 mangoes cost? (a) ₹100 (b) ₹140 (c) ₹882 (d) ₹126
32. 32.If 8 notebooks cost ₹24, how much do 4 notebooks cost? (a) ₹20 (b) ₹96 (c) ₹15 (d) ₹12
33. 33.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹33 (b) ₹165 (c) ₹132 (d) ₹198
34. 34.If 5 kites cost ₹45, how much do 6 kites cost? (a) ₹54 (b) ₹63 (c) ₹46 (d) ₹270
35. 35.If 7 mangoes cost ₹154, how much do 6 mangoes cost? (a) ₹154 (b) ₹924 (c) ₹153 (d) ₹132
36. 36.If 6 pens cost ₹126, how much do 3 pens cost? (a) ₹378 (b) ₹63 (c) ₹84 (d) ₹123
37. 37.If 6 mangoes cost ₹60, how much do 7 mangoes cost? (a) ₹80 (b) ₹61 (c) ₹420 (d) ₹70
38. 38.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 17 days (c) 13 days (d) 25 days
39. 39.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 11 days (d) 3 days
40. 40.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 36 days (b) 18 days (c) 6 days (d) 4 days

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