1. The greatest ratio out of 2:3, 5:4, 3:2 and 4:5 is:
a) 2 : 3
b) 5 : 4
c) 4 : 5
d) 3 : 2
Solution: 3:2 = 1.5 which is the highest among all ratios.
2. 2000 is divided between A and B such that half of A’s part equals one-third of B’s part. What is B’s share?
a) 1000
b) 600
c) 800
d) 1200
Solution: A : B = 3 : 2 → total ratio = 5 → B = 2000×2/5 = 1200.
3. The inverse ratio of 1 : 2 : 3 is:
a) 3 : 2 : 1
b) 2 : 3 : 6
c) 2 : 1 : 3
d) 6 : 3 : 2
Solution: Inverse ratio = 1/1 : 1/2 : 1/3 = 6 : 3 : 2.
4. The smallest ratio among 1:1, 2:1, 1:3 and 3:1 is:
a) 3 : 1
b) 1 : 3
c) 2 : 1
d) 1 : 1
Solution: 1/3 = 0.33 which is the smallest.
5. A, B, C and D share money in the ratio 4:7:9:3. If C gets 720 more than D, find the difference between C and B.
A. 240
B. 480
C. 160
D. 360
Solution: Gap(C−D)=9−3=6 → 6 = 720 → 1 part = 120 → C−B = 2 parts = 240.
6. Two numbers differ by 46 and are in the ratio 5:3. Find the smaller number.
a) 36
b) 63
c) 46
d) 69
Solution: Difference ratio=2 parts=46 → 1 part=23 → smaller = 3×23 = 69.
7. Boys and girls are in the ratio 9:7. If girls are 189, find boys.
a) 126
b) 243
c) 168
d) 147
Solution: 7 parts=189 → 1 part=27 → boys=9×27 = 243.
8. Brass contains copper and zinc in ratio 13:7. In 100 kg brass, zinc is:
a) 35 kg
b) 14 kg
c) 42 kg
d) 70 kg
Solution: Zinc = 7/(13+7) ×100 = 35.
9. Two numbers are in the ratio 7:5 and differ by 360. The greater number is:
a) 1260
b) 1040
c) 900
d) 1500
Solution: Difference ratio=2 parts=360 → 1 part=180 → greater = 7×180 = 1260.
10. If x ∝ 1/(y³−1) and x=4 when y=3, find x when y=9.
a) 1/7
b) 1/8
c) 2/8
d) 3/7
Solution: k = x(y³−1) = 4×26 → x = k/(9³−1) = 104/728 = 1/7.
11. If x ∝ 1/(y³−1) and x=6 when y=3, find x when y=7.
a) 26/58
b) 27/58
c) 26/27
d) 28/57
Solution: k=6×26=156 → x=156/(343−1)=156/342=27/58.
12. If x ∝ 1/(y³−1) and x=8 at y=3, find x at y=6.
a) 208/216
b) 209/216
c) 210/215
d) 208/215
Solution: k=8×26=208 → x=208/(216−1)=208/215.
13. If x ∝ 1/(y³−1) and x=3 at y=4, find x at y=6.
a) 190/216
b) 189/216
c) 189/215
d) 191/215
Solution: k=3×63=189 → x=189/216.
14. Which of the following ratio is smallest?
a) 29 : 31
b) 21 : 52
c) 28 : 42
d) 24 : 59
Solution: 21/52 is the smallest.
15. Three furniture items cost in ratio 3:5:7. Avg price = 15960. Find highest price.
a) 22344
b) 5320
c) 7448
d) 3192
Solution: Total price=15960×3=47880 → 1 part=47880/15=3192 → highest=7×3192=22344.
16. Avg price = 15945. Ratio = 3:5:7. Find highest price.
a) 22323
b) 5315
c) 3189
d) 7441
Solution: Total = 47835 → 1 part = 3189 → highest = 7×3189 = 22323.
17. Which ratio is smallest?
a) 22 : 56
b) 15 : 44
c) 29 : 48
d) 30 : 31
Solution: 15/44 is the smallest.
18. Difference between smallest and largest among 6/7, 4/8, 32/39, 25/27:
a) 23/54
b) 23/58
c) 23/56
d) 23/55
Solution: Largest=6/7, smallest=4/8 → diff = 6/7 − 1/2 = 23/54.
19. Difference between smallest & largest among 4/9, 3/7, 31/37, 12/20:
a) 106/255
b) 106/259
c) 106/258
d) 106/261
Solution: Largest=31/37, smallest=3/7 → diff = 106/258.
20. Which fraction is largest?
a) 63/64
b) 5/26
c) 44/88
d) 5/8
Solution: 63/64 is almost 1 and is the largest.
