__Aptitude Questions (Arithmetic) for Upcoming AAO/SO Exams Set-26__**:**

Dear Readers, Important Practice Aptitude Questions for Upcoming AAO/SO Exams was given here with Solutions. Aspirants those who are preparing for the examination can use this.

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**Directions (Q. 1-10): Study the following information carefully and answer the questions given below:**

**1).**From a pack of 52 cards, 2 cards are drawn randomly. What is the probability that it has one king and one Jack.

a) (7/663)

b) (8/663)

c) (11/663)

d) (13/663)

e) None of these

**2).**In an examination a minimum marks is to be scored in each of the 8 subjects for passing. In how many ways a student can fail?

a) 127

b) 63

c) 255

d) 256

e) None of these

**3).**A certain sum of money amounted to Rs.600 at 55 % in a time in which Rs.800 amounted to Rs.960 at the same rate. If rate of interest is simple then what is the sum?

a) Rs.540

b) Rs.520

c) Rs.500

d) Rs.480

e) Rs.450

**4).**If the difference between the compound interest and simple interest on a certain sum of money at 6% per annum for 2 years is Rs.3.60.What is the sum?

a) Rs.920

b) Rs.925

c) Rs.960

d) Rs.980

e) Rs.1000

**5).**A man can swim at 10 kmph in still water .If the river flows at 3 kmph and, it takes 12 hours more in upstream than to go downstream for the same distance, then how far is the place?

a) 160 km

b) 164 km

c) 170 km

d) 175 km

e) 182 km

**6).**Two trains of length 120 m and 90 m respectively with the same speed pass a static pole in 8 seconds and 6 seconds respectively. In what time they will cross each other if they are moving in opposite directions?

a) 14 seconds

b) 6 seconds

c) 20 seconds

d) 7 seconds

e) None of these

**7).**A train travelling at the speed of 50 kmph leaves from a station. Another train travelling at speed of 60 kmph leaves the same station after 7 hours in the same direction. They will meet after what distance?

a) 1800 km

b) 2100 km

c) 2400 km

d) 2700 km

e) None of these

**8).**A alone would take 6 hours more to complete the job than if both A and B would work together. When B worked alone he took 1.5 hours more to complete the job and A and B worked together. How much time they will take if they work together?

a) 3 hours

b) 4 hours

c) 4.5 hours

d) 5 hours

e) None of these

**9).**A dealer bought an item at 10% discount on its original price. He sold it at 35% more than the original price. What percentage profit did he get?

a) 25%

b) 45%

c) 22.5%

d) 50%

e) 35%

__Answers__**:**

**1). b) 2). c) 3). c) 4). e) 5). e) 6). d) 7). b) 8). a) 9). d)**

__EXPLANATIONS:__

**1.**n(S) =

^{52}C

_{2 }= 51 ร 26

N(E) =

^{ 4}C_{1 }= 4 ร 4P(E) = (16 / 51ร26) = (8 / 663)

**Answer: b)**

**2.**The students can fail in 1, 2, 3, 4, 5, 6, 7, 8 subjects. So the number of ways he can fail is

^{8}C

_{1 }+

^{8}C

_{2 }+

^{8}C

_{3 }+

^{8}C

_{4 }+

^{8}C

_{5 }+

^{8}C

_{6 }+

^{8}C

_{7 }+

^{8}C

_{8 }= 8 + 28 + 56 + 70 + 56 + 28 +8+ 1 = 255

**Answer: c)**

**3.**Interest = 960 – 800 =160

Time = [(160ร100) / (5ร800)] = 4 years

Now, t = 4, r = 5%, Amount = 600

Sum = [(100ร600) / (100+5ร4)] = (60000 / 120) = 500

**Answer: c)**

**4.**Sum = [(Difference ร100ร100) / (6ร6)]

= [(3.6ร100ร100 / 36) =1000

**Answer: e)**

**5.**Let distance be =x

:. (x / 10-3) โ (x / 10+3) = 12

โ (x / 7) โ (x / 13) = 12

โ [(13x-7x) / 91] =12

โ (6x / 91) = 12

X= [(91ร12 / 6] =182km

**Answer: e)**

**6.**Speed of trains = (120 / 8) =15 m/sec

And (90 / 6) =15 m/sec

Relative speed = 15 + 15 = 30 m/sec

Time = [(120 + 90) / 30] = (210 / 30) = 7 seconds

**Answer: d)**

**7.**Let the requires distance be x km.

(x / 50) โ (x / 60) =7

โ [(6x – 5x) / 300] =7

X = 300 ร 7 = 2100km

**Answer: b)**

**8. Answer: a)**

**9.**Let the original price be Rs.100

So he bought it at 10% discount ie Rs.90 and sells it at 35% more than the original rate ie.Rs.135.

Actual profit is 135 – 90 = Rs.45

% profit = (45 / 90) ร 100 = 50%

**Answer: d**

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