Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 269 · 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.₹528 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹192 (b) ₹264 (c) ₹48 (d) ₹336
2. 2.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 13 days (c) 16 days (d) 1 day
3. 3.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 6 days (d) 15 days
4. 4.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹95 (b) ₹114 (c) ₹38 (d) ₹76
5. 5.If 7 mangoes cost ₹161, how much do 8 mangoes cost? (a) ₹1288 (b) ₹162 (c) ₹184 (d) ₹207
6. 6.If 9 pens cost ₹117, how much do 10 pens cost? (a) ₹1170 (b) ₹143 (c) ₹118 (d) ₹130
7. 7.If 9 notebooks cost ₹225, how much do 4 notebooks cost? (a) ₹900 (b) ₹125 (c) ₹220 (d) ₹100
8. 8.₹160 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹128 (b) ₹80 (c) ₹32 (d) ₹160
9. 9.If 8 notebooks cost ₹72, how much do 3 notebooks cost? (a) ₹216 (b) ₹36 (c) ₹67 (d) ₹27
10. 10.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 28 days (c) 19 days (d) 7 days
11. 11.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹322 (b) ₹46 (c) ₹276 (d) ₹230
12. 12.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 9 days (d) 45 days
13. 13.If 6 pens cost ₹60, how much do 2 pens cost? (a) ₹30 (b) ₹56 (c) ₹20 (d) ₹120
14. 14.₹196 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹98 (b) ₹84 (c) ₹28 (d) ₹112
15. 15.If 4 kites cost ₹16, how much do 5 kites cost? (a) ₹17 (b) ₹20 (c) ₹24 (d) ₹80
16. 16.If 6 pens cost ₹54, how much do 9 pens cost? (a) ₹486 (b) ₹57 (c) ₹90 (d) ₹81
17. 17.If 9 notebooks cost ₹216, how much do 4 notebooks cost? (a) ₹120 (b) ₹864 (c) ₹211 (d) ₹96
18. 18.If 7 pens cost ₹70, how much do 11 pens cost? (a) ₹74 (b) ₹120 (c) ₹770 (d) ₹110
19. 19.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹55 (b) ₹30 (c) ₹80 (d) ₹10
20. 20.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 14 days (d) 11 days
21. 21.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹61 (b) ₹15 (c) ₹75 (d) ₹60
22. 22.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 4 days (d) 11 days
23. 23.If 6 mangoes cost ₹48, how much do 12 mangoes cost? (a) ₹54 (b) ₹104 (c) ₹576 (d) ₹96
24. 24.8 workers can build a wall in 15 days. How many days will 4 workers take, working at the same speed? (a) 19 days (b) 30 days (c) 31 days (d) 11 days
25. 25.If 2 pens cost ₹6, how much do 6 pens cost? (a) ₹10 (b) ₹18 (c) ₹21 (d) ₹36
26. 26.If 5 notebooks cost ₹110, how much do 10 notebooks cost? (a) ₹1100 (b) ₹220 (c) ₹242 (d) ₹115
27. 27.₹400 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹400 (b) ₹200 (c) ₹40 (d) ₹360
28. 28.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 25 days (d) 17 days
29. 29.If 4 notebooks cost ₹40, how much do 7 notebooks cost? (a) ₹80 (b) ₹280 (c) ₹43 (d) ₹70
30. 30.₹516 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹215 (b) ₹258 (c) ₹43 (d) ₹301
31. 31.₹126 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹36 (b) ₹90 (c) ₹18 (d) ₹63
32. 32.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 15 days (d) 24 days
33. 33.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 17 days (c) 36 days (d) 11 days
34. 34.If 4 kites cost ₹52, how much do 8 kites cost? (a) ₹117 (b) ₹416 (c) ₹104 (d) ₹56
35. 35.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹115 (b) ₹92 (c) ₹46 (d) ₹138
36. 36.If 6 notebooks cost ₹18, how much do 5 notebooks cost? (a) ₹17 (b) ₹90 (c) ₹18 (d) ₹15
37. 37.If 6 mangoes cost ₹132, how much do 2 mangoes cost? (a) ₹66 (b) ₹128 (c) ₹44 (d) ₹264
38. 38.If 6 pens cost ₹84, how much do 7 pens cost? (a) ₹112 (b) ₹85 (c) ₹588 (d) ₹98
39. 39.₹125 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹50 (b) ₹75 (c) ₹25 (d) ₹100
40. 40.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹48 (b) ₹56 (c) ₹8 (d) ₹40

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