1. A certain sum of money at certain rate of interest becomes Rs.3420 after 2 years and at same rate after two and a half years becomes Rs.3525. Find the rate percent per annum.

A. 8.5% B. 8% C. 7% D. 10% E. 11%

2. A sum of money becomes RS.35,280 after 2 years and Rs.37,044 after 3 years when lent on compound interest. Find the principal amount

A. Rs.32,000 B. Rs.28,000 C. Rs.31,000 D. Rs.32,500 E. None of these

3. A person sell two horses for rupees 480 each. On the first horse he gains 25 percent and on the second horse he losses 25 percent. Find the percent gain or loss in the transaction

A. loss 6.75% B. gain 6.75% C. loss 6.25% D. gain 6.25% E. None of these

4. Ashwin has to travel from one point to another point in a certain time. Travelling at a speed of 6kmph he reaches 40m late and travelling at a speed of 8kmph he reaches 12 m earlier.What is the distance between this two points ?

A. 27 km B. 18 km C. 5 km D. 21 km E. None of these

5. Two trains A and B start from two places P and Q towards Q and P respectively. After passing each other they take 4 hours 48 minutes and 3 hours and 20 minutes to reach Q and P respectively. If the train from P is moving at 45 km/h then find the speed of other train

A. 69 km/h B. 74 km/h C. 54 km/h D. 64 km/h E. 72 km/h

6. Ronit's age is 10 years more than Rohit's age. Also Ronit was twice old as Rohit 15 years ago. What will be the age of Ronit 6 years after?

A. 41 B. 40 C. 35 D. 45 E. 38

7. The average age of the group having 3 members is 84. One more person joins the group and now the average becomes 80. Now a fifth person comes whose age is 3 years more than that of fourth person replaces the first person. After this the average age of the group becomes 79. What is the weight of the first person?

A. 75 B. 65 C. 68 D. 82 E. 85

8. A, B and C can alone complete a work in 10, 12 and 15 days respectively. A and C started the work and after working for 4 days, A left and B joined. In how many days the total work was completed?

A. 6[latex]\frac{5}{9}[/latex] B. 6[latex]\frac{2}{9}[/latex] C. 6 days D. 5[latex]\frac{4}{9}[/latex] E. 7[latex]\frac{2}{9}[/latex]

9. There are 4 filling pipes and 3 emptying pipes capable of filling and emptying in 12 minutes and 15 minutes respectively. If all the pipes are opened together and as a result they fill 10 litres of water per minute. Find the capacity of the tank.

A. 65 ltr B. 70 ltr C. 75 ltr D. 80 ltr E. None of these

10. Divide Rs.2340 into three parts, such that first part be double that of second part and second part be 1/3 of the third part.Find the Third part amount?

A. Rs.780 B. Rs.1170 C. Rs.750 D. Rs.390 E. None of these

DIRECTION(11-15): Each of the following number series, a wrong number is given. Find out that number.
11. 3, 5, 13, 43, 178, 891, 5353

A. 43 B. 178 C. 891 D. 5353 E. None of these

12. 90720, 10080, 1440, 240, 48, 10, 4

A. 240 B. 48 C. 1440 D. 10 E. None of these

13. 3, 5, 10, 12, 17, 23, 24

A. 5 B. 17 C. 24 D. 23 E. None of these

14. 1, 11, 38, 78, 175, 301

A. 11 B. 78 C. 175 D. 301 E. None of these

15. 7, 39, 85, 179, 211, 369, 879

A. 369 B. 211 C. 179 D. 879 E. None of these

DIRECTIONS(16-20): In the following questions two equations numbered I and II are given. You have to solve both the equations and give the answer
16. (x + 2)(x + 1) = (x – 2)(x – 3) (y + 3)(y + 2) = (y – 1)(y – 2)

A. x > y B. x < y C. x [latex]\geq[/latex] y D. x [latex]\leq[/latex] y E. x = y or relation cannot be established

17. 12x² + 29x + 14 = 0 y² + 9y + 18 = 0

A. x > y B. x < y C. x [latex]\geq[/latex] y D. x [latex]\leq[/latex] y E. x = y or relation cannot be established

18. 5x² – 18x + 9 = 0 3y² + 5y – 2 = 0

A. x > y B. x < y C. x [latex]\geq[/latex] y D. x [latex]\leq[/latex] y E. x = y or relation cannot be established

19. [latex]{17}^{2}[/latex] + 144 ÷ 18 = x [latex]{26}^{2}[/latex] - 18 × 18 = y

A. x > y B. x < y C. x [latex]\geq[/latex] y D. x [latex]\leq[/latex] y E. x = y or relation cannot be established

20. [latex]{30x}^{2}[/latex] + 11x + 1 = 0 [latex]{42y}^{2}[/latex] + 13y + 1 = 0

A. x > y B. x < y C. x [latex]\geq[/latex] y D. x [latex]\leq[/latex] y E. x = y or relation cannot be established

DIRECTION(21-25): What approximate value should come in place of the question mark (?) in the following questions? (You are not expected to calculate the exact value.)
21. 16.003 × 29.998 – 40.002 × 9.009 = ?

A. 110 B. 118 C. 120 D. 124 E. 130

22. 420.009 ÷ 13.998 + 11.997 – 17.0023 =?

A. 23 B. 24 C. 25 D. 26 E. 27

23. 41% of 801 – 150.17 = ? – 57% of 910

A. 693 B. 694 C. 697 D. 707 E. None of these

24. 1235.092 + 4532.998 – ? + 1279.991 = 4000.001

A. 2048 B. 3048 C. 3648 D. 4048 E. None of these

25. ([latex]\frac{1}{2}[/latex]) × ([latex]\frac{1}{17.01}[/latex]) × 289 × ? = 4.001 × 2.01

A. [latex]\frac{16}{17}[/latex] B. [latex]\frac{14}{17}[/latex] C. [latex]\frac{15}{17}[/latex] D. [latex]\frac{13}{17}[/latex] E. [latex]\frac{17}{16}[/latex]

DIRECTIONS(26-30): These questions are based on the following bar graph and line graph. The following bar graph gives the total population of five villages and the number of males in each of the five villages.
The following line graph gives the percentage of literates amount males, for each of the five villages.
26. In which village is the number of females as a percentage of the total population, the lowest?

A. A B. B C. C D. D E. E

27. What is the ratio of the number of illiterate males in B to that in C?

A. 24 : 5 B. 7 : 16 C. 9 : 13 D. 11 : 19 E. None of these

28. What is the average number of literate males per village?

A. 32240 B. 24420 C. 28120 D. 29430 E. None of these

29. In how many villages is the number of illiterate males, as a percentage of the total population, more than 21%

A. 1 B. 2 C. 3 D. 4 E. None of these

30. In which village is the number of literate males, as a percentage of the total population, the lowest?

A. A B. D C. B D. C E. E

DIRECTIONS(31-35): Study the following graph to answer the following questions
Total number of students = 90,000

31. The no of girls students in District T is what % of the total no students in District Q ?

A. 47% B. 31% C. 37% D. 40% E. 43%

32. What is the average number of boys students in all the districts together?

A. 7533 B. 7353 C. 7550 D. 7300 E. 7800

33. What is the difference between the number of girls students in District P and the total number of students in District R?

A. 11000 B. 9700 C. 10000 D. 10100 E. 10200

34. What is the ratio of the no of boys in District U to the total no of girls in District S ?

A. 43:76 B. 50:75 C. 53:80 D. 80:53 E. 54:82

35. What is the total no of students in District P,R and T ?

A. 46000 B. 46800 C. 48600 D. 45000 E. 45500

Answers
Solution: 1-10
1. Answer - C Explanation: Amount after 2.5 yrs = 3525, after 2 yrs = 3420 So SI for half yr = 3525 – 3420 = 105, so for 1 yr SI = 105 × 2 = 210 P + 2 × SI = 3420 So P = 3420 – 2 × 210 = 3000 So 3000 × r × 2/100 = 420
2. Answer - A Explanation: Divide both equations, [1 + r/100] = 37044/35280 = 21/20 So P[21/20]2 = 35280
3. Answer - C Explanation: When the same quantity is sold at the same price and percent gain and loss are the same then there is always loss occurred. To calculate the loss per cent = [latex]{Common loss or gain}^{2}[/latex]/10 i.e.,[latex]{25/10}^{2}[/latex] = 6.25% loss
4. Answer - D Explanation: d/6 -40/60 = d/8 + 12/60 d/6 - d/8 = 12/60 - 40/60 2d/48 = 52/60 D= 52 × 40/60 × 2 = 20.8 = 21km
5. Answer - C Explanation: Speed of 2nd train = Speed of first train × ( [latex]{Time taken by 1st train after meeting}^{1/2}[/latex] / [latex]{Time taken by 2nd train after meeting}^{1/2}[/latex])
6. Answer - A Explanation: Rohit = x, Ronit = x+10 (x + 10) – 15 = 2 (x – 15) Solve, x = 25 Ronit's 6 years after = x + 10 + 6
7. Answer - A Explanation: Let the ages of these are A, B, C, D, E So A + B + C = 84 × 3 = 252 And A + B + C + D = 80 × 4 = 320 So D = 320 – 252 = 68, so E = 68 + 3 = 71 Now B + C + D + E = 79 × 4 = 316 (A + B + C + D) – (B + C + D + E) = 320 – 316 So A – E = 4, so A = 71+ 4
8. Answer - B Explanation: (A + C) = [latex]\frac{ 1 }{10}[/latex] + [latex]\frac{ 1 }{15}[/latex] = [latex]\frac{ 1 }{6}[/latex]. They worked for 4 days so did [latex]\frac{ 1 }{6}[/latex] × 4 = [latex]\frac{2 }{3}[/latex]rd of work Remaining Work = 1 - [latex]\frac{ 2 }{3}[/latex] = [latex]\frac{ 1 }{3}[/latex] Now A left, B and C working (B + C) = ([latex]\frac{ 1 }{12}[/latex] + [latex]\frac{ 1 }{15}[/latex]) = [latex]\frac{ 9 }{60}[/latex] = [latex]\frac{ 3 }{20}[/latex]. They worked for x days and completed 1/3rd of work so 3/20 × x = 1/3, so x = 20/9 days Total = 4 + [latex]\frac{ 20 }{9}[/latex]
9. Answer - C Explanation: ([latex]\frac{4}{12}[/latex] - [latex]\frac{3}{15}[/latex]) × t = 1 t = [latex]\frac{15}{2}[/latex] minute – in this time the tank will be filled. So the capacity = [latex]\frac{15}{2}[/latex] × 10 = 75 litre
10. Answer - B Explanation: First: Second: Third = 2:1:3 Third part = 3 × [latex]\frac{2340}{6}[/latex] = 1170
Solution: 11-15
11. Answer - B Explanation: 3 × 1 + 2 = 5 5 × 2 + 3 = 13 13 × 3 + 4 = 43….. Correct Number: 177
12. Answer - D Explanation: 4 ×3 = 12 12 × 4 = 48 48 × 5 = 240….. Correct Number: 12
13. Answer - E Explanation: First series: 3, 10, 17, 24 (increased by 7) Second Series: 5, 14, 23 (increased by 9) Wrong Number: 12 Correct Number: 14
14. Answer - B Explanation: 1 + [latex]{3}^{2}[/latex] + 1 = 11 11 + [latex]{5}^{2}[/latex] + 2 = 38 38 + [latex]{7}^{2}[/latex] + 3 = 90 90 + [latex]{9}^{2}[/latex] + 4 = 175 175 + [latex]{11}^{2}[/latex]+ 5 = 301
15. Answer - D Explanation: 7 × 2 + 3 = 17 17 × 2 + 5 = 39 39 × 2 + 7 = 85 85 × 2 + 9 = 179 179 × 2 + 11 = 369 369 × 2 + 13 = 751
Solution: 16-20
16. Answer - A Explanation: (x + 2) (x + 1) = (x – 2)(x – 3) x = [latex]\frac{1}{2}[/latex] = 0.5 (y + 3)(y + 2) = (y – 1)(y – 2) y = -[latex]\frac{1}{2}[/latex] = -0.5
17. Answer - A Explanation: 12x² + 29x + 14 = 0 x = – 1.75, – 0.6 y² + 9y + 18 = 0 y = –6, –3
18. Answer - A Explanation: 5x² – 18x + 9 = 0 x = 0.6, 3 3y² + 5y – 2 = 0 y = 0.33, –2
19. Answer - B Explanation: [latex]{17}^{2}[/latex] + 144 ÷ 18 = x x = 297 [latex]{26}^{2}[/latex] – 18 × 21 = y y = 676 – 378 = 29
20. Answer - D Explanation: [latex]{30x}^{2}[/latex] + 11x + 1 = 0 [latex]{30x}^{2}[/latex] + 6x + 5x + 1 = 0 x = – 0.16, –0.19 [latex]{42y}^{2}[/latex] + 13y + 1 = 0 [latex]{42y}^{2}[/latex] + 6y + 7y + 1 = 0 y = –0.14, –0.16 Put on number line –0.19, –0.16, –0.16, –0.14
Solution: 21-25
21. Answer - C Explanation: 16×30 – 40×9 = 480 – 360 = 120
22. Answer - C Explanation: 420/14 + 12 – 17 = 25
23. Answer - C Explanation: [latex]\frac{41}{100}[/latex] × 800 - 150 = x - [latex]\frac{57}{100}[/latex] × 910
24. Answer - B Explanation: ? = 7048 – 4000 = 3048
25. Answer - A Explanation: ? = [latex]\frac{4 × 2 × 2 }{17}[/latex] = [latex]\frac{16 }{17}[/latex]
Solution: 26-30
26. Answer - B Explanation: Percentage of females as a percentage of total population in A = [latex]\frac{24000}{64000}[/latex] × 100 = 37.5% B = [latex]\frac{24000}{72000}[/latex] × 100 = 33[latex]\frac{1}{3}[/latex]% C = [latex]\frac{24000}{54000}[/latex] × 100 = 44[latex]\frac{4}{9}[/latex]% D = [latex]\frac{30000}{80000}[/latex] × 100 = 37.5% E = [latex]\frac{36000}{60000}[/latex] × 100 = 60%
27. Answer - A
28. Answer - C Explanation: The required average = (40000 × [latex]\frac{80}{100}[/latex] + 48000 × [latex]\frac{70}{100}[/latex] + 30000 × [latex]\frac{90}{100}[/latex] + 50000 × [latex]\frac{60}{100}[/latex] + 24000 × [latex]\frac{75}{100}[/latex] x [latex]\frac{ 1 }{5}[/latex] = [latex]\frac{ 140600 }{5}[/latex] = 28120
29. Answer - A Explanation: Percentage of illiterate males in the given villages is as follows. A = [latex]\frac{8000}{64000}[/latex] × 100 = 12.5% B = [latex]\frac{14400}{72000}[/latex] × 100 = 20% C = [latex]\frac{3000}{54000}[/latex] × 100 = 5.55% D = [latex]\frac{20000}{80000}[/latex] × 100 = 25%
30. Answer - E Explanation: % of literate males in A = [latex]\frac{32000}{64000}[/latex] × 100 = 50% B = [latex]\frac{33600}{72000}[/latex] × 100 = 46[latex]\frac{2}{3}[/latex]% C = [latex]\frac{27000}{54000}[/latex] × 100 = 50% D = [latex]\frac{30000}{80000}[/latex] × 100 = 37.5% D = [latex]\frac{18000}{60000}[/latex] × 100 = 30% It is the lowest in village E.
Solution: 31-35
31. Answer - B Explanation: No of girls in T = (12 × [latex]\frac{90000}{100}[/latex]) – 7200 = 10800 – 7200 = 3600 Total no of students in Q = 13 x [latex]\frac{90000}{100}[/latex] = 11700 % = (3600 × [latex]\frac{100}{1700}[/latex]) = 30.77% = 31%
32. Answer - A Explanation: ([latex]\frac{6500 + 8900 + 5500 + 9100 + 7200 + 8000}{6}[/latex]) = [latex]\frac{45200}{6}[/latex]
33. Answer - D Explanation: Total no. of students in R = ([latex]\frac{22 × 90000 }{100}[/latex]) = 19800 No. of girls in P = ([latex]\frac{18 × 90000 }{100}[/latex]) - 6500 = 9700 Difference = 19800 – 9700 = 10100
34. Answer - D Explanation: Boys in U = 8000 Girls in S = (16× [latex]\frac{18 × 90000 }{100}[/latex]) – 9100 = 5300 80:53
35. Answer - B Explanation: P = 18 × ([latex]\frac{ 90000 }{100}[/latex]) = 16200 R = 22 × ([latex]\frac{ 90000 }{100}[/latex]) = 19800 T = 12 × ([latex]\frac{ 90000 }{100}[/latex]) = 10800 Total = 46,800