1. In how many ways can the letters of the word INDIA be arranged, such that all vowels are never together?

A. 48 B. 42 C. 28 D. 36

Answer: Option B
Explanation: First, we find out the number of times a particular letter occurs in the given word: 2 – I 1 – A 1 – D 1 – N => Total number of solutions minus the number of times all three vowels are together. Now, using the concept of permutation and combination: => Divide the possible combination by 2! because it occurs twice and replacing one by another will cause no difference in the word. => Total number of words that can be formed: 5!/2! => Total number of words that can be formed keeping all the vowels together: 3! 3!/2! => 60 – 18 = 42
2. The income of A is 25% more than the income of B. What is the income of B in terms of income of A?

A. 80% B. 75% C. 78.66% D. 71.25%

Answer: Option D
Explanation: One of the most basic questions. Let the income of B be 100. The income of A is 25% more than the income of B which means Income of A becomes 125 Now income of B in terms of A = 100/125 *100 = 80%
3. A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A?

A. 26.2 km B. 25.7 km C. 23.2 km D. 26.67 km

Answer: Option D
Explanation: Distance travelled by each of them is to be made equal. => Distance traveled walking = Distance covered cycling. Let after 4 hours of walking, A walk for x hours more before B catches up with him. => Distance = Speed * Time (4+x)4 = 10x x = 8/3 Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67
4. If one is added to the numerator of the fraction it becomes one. If one is added to the denominator of the fraction it becomes 1/2. The fraction is?

A. [latex]\frac{1}{2}[/latex] B. [latex]\frac{3}{5}[/latex] C. [latex]\frac{2}{3}[/latex] D. [latex]\frac{2}{5 }[/latex]

Answer: Option C
Explanation: Let the fraction be [latex]\frac{X}{Y }[/latex]. => [latex]\frac{X + 1}{Y}[/latex] = 1 => x+1 = y—(1) [latex]\frac{X}{Y - 1 }[/latex] = [latex]\frac{1}{2 }[/latex] => 2x = (y+1)—(2) =>Equating (1) and (2) => x+1 = 2x-1 =>x=2 Substituting the value of x in (1) =>y=3 =>2/3
5. A boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. What is the speed of current?

A. 4 kmph B. 6 kmph C. 5 kmph D. 8 kmph

Answer: Option C
Explanation: Speed of the boat in still water: 15 km/hr Speed of boat downstream: (15+x)km/hr where x is the speed of the current. The boat travels 30 km downstream and then 30 km upstream and takes [latex]\frac{9}{2 }[/latex] hours. Total time= Time taken to travel downstream + Time is taken to travel upstream => 4/5= (30/(15+x))+(30/(15-x)) =>x= 5

Directions ( 1- 5): Find the odd one out 1. 125, 106, 88, 76, 65, 58, 53

A. 88 B. 106 C. 125 D. 76

Answer: Option A
Explanation: This sequence represents a series in which from the reverse order a prime number is added: 53+5=58 58+7=65 65+11=76 76+13=89 89+17=106 106 + 19 = 125 Hence 88 is the answer.
2. What is the CP of Rs 100 stock at 4 discount, with 1/5% brokerage?

A. 99.6 B. 96.2 C. 97.5 D. 98.25

Answer: Option B
Explanation: Use the formula, CP= 100 – discount + brokerage% CP= 100 - 4 +[latex]\frac{1}{5 }[/latex] 96.2 Thus the CP is Rs 96.2.
3. A pipe is 30 m long and is 45% longer than another pipe. Find the length of the other pipe.

A. 20.68 B. 20 C. 20.12 D. 20.5

Answer: Option B
Explanation: Let length of other pipe be X According to question, 30 = [latex]\frac{45}{100 }[/latex] X + X 30 = 0.45X + X 30 = 1.45 X X= [latex]\frac{30}{1.45 }[/latex] X = 20.68m Thus the length of the other pipe is 20.68 meters.
4. 15th august 2010 was which day of the week?

A. Thursday B. Friday C. Wednesday D. Sunday

Answer: Option D
Explanation: 15th August 2010 can be written as 2009 + days from 1st January 2010 to 15th August 2010. => Total number of odd days in 400 years = 0 Hence, the total number of odd days in 2000 years = 0 (as 2000 is a perfect multiple of 400) Odd in days in the period 2001-2009: 7 normal years + 2 leap yeas => (7*1) + (2*2) = 11 => Odd days will be 11- (7*1) = 4 Days from January 1 to August 15 in 2010: 31+28+31+30+31+30+31+15 = 227 days. = 32 weeks and 3 days, this gives additional 3 odd days. => Total odd days= 3+4=7 => 7 odd days=1 week= 0 odd days => 0 odd days= Sunday Thus, 15th August 2010 was a Sunday.
5. A boatman rows 96 km downstream in 8 hours with a stream speed of 4kmph. How much time will he take to cover 8km upstream?

A. 4 hours B. 6 hours C. 2 hours D. 1 hours

Answer: Option C
Explanation: Speed = distance/time Speed downstream: [latex]\frac{96}{8 }[/latex] km/hr = 12kmph Speed of stream = 4kmph Effective speed of boat = (12-4) kmph = 8kmph Distance to be traveled upstream= 8 km Speed upstream = boat speed-current speed = 8-4 kmph = 4 kmph Time taken = [latex]\frac{Distance}{Speed }[/latex] = [latex]\frac{8}{4 }[/latex] hours = 2 hours Thus it will take 2 hours to go upstream.

1. While calculating the edge of a square, a worker makes an error of 2% in excess. What % error does he make in calculating area? (%)

A. 4.04 B. 4 C. 40.4 D. 4.004

Answer: Option A
Explanation: Given Error = 2% while measuring the side of a square. If the correct value of the side of the square is 100, the measured value: => 100 + 2% *100 = 100+2=102 The area of a square with edge 100 = side*side => 100*100 => 10000 The area of a square with side 102 = 102*102= 10404 Error in area calculation = 10404-1000 = 404 % error= [latex]\frac{404}{10000 }[/latex]*100 = 4.04%
2. Akash and Akshay are business partners. Akash invests Rs 35,000 for a period of 8 months and Akshay invests Rs 42,000 for a period of 10 months. Out of a total profit of Rs 31,570 what is Akash’s share?

A. Rs 12,420 B. Rs 18,040 C. Rs 18,942 D. Rs 12,628

Answer: Option D
Explanation: For a given business profit is directly dependent upon the capital invested and the time of investment. => Ratio of shares of Akash and Akshay becomes: (35,000*8)/(42,000*10) = [latex]\frac{2}{3 }[/latex] =>% of profit belonging to Akash: [latex]\frac{2}{3 + 2 }[/latex]*(31,570) =>Rs 12,768
3. In what ratio must one add water to milk so as to gain 16.666% on the selling this mixture at the cost price?

A. 1:6 B. 1:3 C. 6:1 D. 3:1

Answer: Option A
Explanation: To start off this question let us assume that cost price of 1 litre milk is Rs 1 No need to make a mixture and sell this mixture at 1 Rs per liter such that the total gain on the mixture is 16.667%. Therefore, CP of 1 liter of the mixture becomes (quantity of milk)/ (quantity of mixture containing 1 L milk)*(the price of 1-liter milk). =>[latex]\frac{(100}{(100+50/3) }[/latex]*1 =>CP of 1-litre milk of mixture: Rs [latex]\frac{5}{6 }[/latex] As the price of any amount of water is zero, and as 1-liter milk costs Rs 1.5/6litre of the mixture will comprise entirely of cost of milk which means,1 liter of the mixture will contain 5/6th amount of milk. =>Water is added in the ratio of (1-[latex]\frac{5}{6 }[/latex])= [latex]\frac{1}{6 }[/latex]
4. Ram can finish a puzzle in 3 hours and Shyam can do the same in 2 hours. Both of them finish the puzzle and get 15 candies. What is Ram’s share?

A. 3 B. 6 C. 11 D. 12

Answer: Option B
Explanation: The question is based on efficiency to do work. Ram can finish a puzzle in 3 hours. Shyam can finish the puzzle in 2 hours. =>In one hour Ram can finish 1/3rd of a puzzle =>In one hour Shyam can finish half the puzzle A total of 15 candies are to be shared amongst both of them Hence Ram’s share must be = ((Work done by Ram in 1 hour)/(Work is done by Shyam in one hour)+(Work done by Ram in an hour))*15 => 1/3/((1/2)+(1/3))*15 => (1/3/(5/6))*15 => [latex]\frac{6}{15 }[/latex]*(15) =>6 candies
5. A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?

32 B. 20 C. 24 D. 16

Answer: Option A
Explanation: Let cost price of lemons be x. Selling price of lemons becomes CP - loss. =>SP=x-(20/100)x =>40=x(80/100) =>50 So 45 lemons cost Rs 50 Cost of 1 lemon = [latex]\frac{50}{45 }[/latex] Rs Cost of 24 lemons = ([latex]\frac{50}{45}[/latex])*24 =80/3 Rs Selling Price of 24 lemons = ([latex]\frac{80}{3 }[/latex])+([latex]\frac{20}{100 }[/latex])([latex]\frac{80}{3 }[/latex])=Rs 32