Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 544 · 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 5 notebooks cost ₹50, how much do 8 notebooks cost? (a) ₹53 (b) ₹90 (c) ₹80 (d) ₹400
2. 2.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹228 (b) ₹190 (c) ₹266 (d) ₹38
3. 3.If 7 kites cost ₹28, how much do 3 kites cost? (a) ₹84 (b) ₹16 (c) ₹24 (d) ₹12
4. 4.If 8 notebooks cost ₹128, how much do 12 notebooks cost? (a) ₹132 (b) ₹1536 (c) ₹192 (d) ₹208
5. 5.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹56 (b) ₹63 (c) ₹35 (d) ₹7
6. 6.If 6 notebooks cost ₹144, how much do 8 notebooks cost? (a) ₹1152 (b) ₹216 (c) ₹146 (d) ₹192
7. 7.₹297 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹81 (b) ₹243 (c) ₹27 (d) ₹216
8. 8.If 4 kites cost ₹64, how much do 12 kites cost? (a) ₹72 (b) ₹768 (c) ₹192 (d) ₹208
9. 9.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 26 days (c) 27 days (d) 28 days
10. 10.If 7 notebooks cost ₹49, how much do 10 notebooks cost? (a) ₹70 (b) ₹52 (c) ₹490 (d) ₹77
11. 11.₹450 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹405 (b) ₹450 (c) ₹225 (d) ₹45
12. 12.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 20 days (b) 12 days (c) 8 days (d) 5 days
13. 13.If 2 kites cost ₹36, how much do 12 kites cost? (a) ₹216 (b) ₹46 (c) ₹234 (d) ₹432
14. 14.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹22 (b) ₹198 (c) ₹121 (d) ₹44
15. 15.If 2 notebooks cost ₹44, how much do 3 notebooks cost? (a) ₹88 (b) ₹45 (c) ₹132 (d) ₹66
16. 16.If 6 mangoes cost ₹96, how much do 8 mangoes cost? (a) ₹128 (b) ₹98 (c) ₹144 (d) ₹768
17. 17.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 1 day (c) 7 days (d) 2 days
18. 18.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 5 days (c) 6 days (d) 7 days
19. 19.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 1 day (d) 3 days
20. 20.9 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 10 days (d) 3 days
21. 21.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 12 days (d) 7 days
22. 22.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 3 days (d) 4 days
23. 23.If 8 mangoes cost ₹80, how much do 7 mangoes cost? (a) ₹79 (b) ₹70 (c) ₹80 (d) ₹560
24. 24.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 52 days (d) 53 days
25. 25.If 5 pens cost ₹60, how much do 2 pens cost? (a) ₹36 (b) ₹120 (c) ₹24 (d) ₹57
26. 26.₹330 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹30 (b) ₹120 (c) ₹210 (d) ₹165
27. 27.If 6 pens cost ₹48, how much do 4 pens cost? (a) ₹40 (b) ₹46 (c) ₹32 (d) ₹192
28. 28.If 3 pens cost ₹33, how much do 2 pens cost? (a) ₹22 (b) ₹66 (c) ₹33 (d) ₹32
29. 29.If 2 mangoes cost ₹16, how much do 11 mangoes cost? (a) ₹176 (b) ₹88 (c) ₹96 (d) ₹25
30. 30.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹250 (b) ₹25 (c) ₹100 (d) ₹225
31. 31.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 10 days (d) 8 days
32. 32.₹91 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹13 (b) ₹79 (c) ₹78 (d) ₹91
33. 33.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 12 days (c) 2 days (d) 18 days
34. 34.If 5 pens cost ₹45, how much do 3 pens cost? (a) ₹135 (b) ₹36 (c) ₹43 (d) ₹27
35. 35.If 5 notebooks cost ₹110, how much do 8 notebooks cost? (a) ₹880 (b) ₹198 (c) ₹176 (d) ₹113
36. 36.If 2 notebooks cost ₹48, how much do 5 notebooks cost? (a) ₹240 (b) ₹120 (c) ₹51 (d) ₹144
37. 37.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 16 days (c) 11 days (d) 15 days
38. 38.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹198 (b) ₹33 (c) ₹165 (d) ₹231
39. 39.₹221 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹17 (b) ₹153 (c) ₹68 (d) ₹170
40. 40.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 17 days (c) 34 days (d) 33 days

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