31. Kailash faces towards North. Turning to his right, he walks 25 meters. He then turns to his left and walks 30 meters. Next, he moves 25 meters to his right. He then turns to his right again and walks 55 meters. Finally he turns to the right and moves 40 meters. In which direction is he now from his starting point?
Answer:
Explanation:Facing north turns towards right and walks 25km=east Then turns towards left walks 30 m=north
Again he turns towards his right and walks 25m=north east
He moves towards his right and walks 55m=south Finally he turns right and walks 40m=south east.
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32. A group of friends Tom, Tim, Dick, Diana, Harry, and Harriet go out to a fair three hundred meters from the McDonalds which is five Km away. They see a weighing machine and decide to have some fun. However the girls refuse to step on the weighing machine. So Tom, Dick and harry, weigh themselves in a particular order. First Tom, Dick, and Harry weigh themselves individually and then tom and Dick, Dick and Harry, Tom and Harry and then Tom, Dick and harry together respectively. The recorded weight for the last measure is 158 kgs. The average of all the 7 measures is
Answer:
Explanation:Let tom,dick and harry be a, b and c.
Now there is totally 7 rounds of weight measure. First Tom, Dick, and Harry weigh themselves individually and then Tom and Dick, Dick and Harry,
Tom and Harry and then Tom, Dick and Harry together respectively.
Sum of total 7 rounds written as, a+b+c+(a+b)+(b+c)+(c+a)+(a+b+c) = 4(a+b+c) 4*158=632
Average of 7 weighing is 632/7=90.29 kg
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33. The pacelength P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm. The formula applies to Bernard's walking. Calculate Bernard's walking speed kmph.
Answer:
Explanation:n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm.
Number of steps in one minute = 144*1.64
Distance travelled in 1 minute = 144*1.64*1.64 metres Distance travelled in one hr = 144*1.64*1.64*60/1000 km = 23.24 km approx
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34. Arun was all bent on building a new house. He carefully got the blue print of his house designed by his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many such tiles should Arun buy?
Answer:
Explanation:27*48/2*3=216
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35. Janta Airline has a free luggage allowance for its passengers. If any passenger carries excess luggage, it is charged at a constant rate per kg. The total luggage charge paid by Ravind Jekriwal and Pranas Shubhan is Rs.1100. If both Ravind and Pranas had carried luggage twice the weight than they actually did, their luggage charges would have been Rs.2000 and Rs.1000 respectively. What was the charge levied on Ravind's luggage?
Answer:
Explanation:Let the free luggage allowance be ‘f' kg. Let the weight of the luggage carried by Ravind be ‘r' kg and the
weight of the luggage carried by Pranas be ‘p' kg. Thus, the excess luggage weights carried by Ravind and Pranas respectively are (r - f) kg and (p - f) kg.
Thus, the total luggage charge for both would be (r - f) k + (p - f) k if k is the charge per kg.
Thus, (r - f) k + (p - f) k = 1100.
(r + p - 2f) k = 1100 (1)
If Ravind carried twice the luggage weight he actually did, i.e., if he carried 2r kg, then the excess luggage weight he carried would have been 2r - f and the corresponding charge would have been (2r - f) k.
Therefore, (2r - f) k = 2000 (2)
Likewise, If Pranas carried twice the luggage he actually did i.e., if he carried 2p kg, then the excess luggage he carried would have been 2p -f and the corresponding charge would have been (2p - f) k.
Therefore, (2p - f) k = 1000 (3)
Adding (2) and (3) and simplifying, we get, (r + p - f) k = 1500 (4)
Dividing (4) by (1) and simplifying, we get, 19f = 4r + 4p (5)
Dividing (2) by (3) and simplifying, we get,
-f = 2r - 4p (6)
Solving (5) and (6) for r, we get, r = 3f (7)
Subtracting (1) from (4) and simplifying, we get, fk = 400.
Ravind's luggage charge = (r - f) k.
But, according to equation (7), r = 3f. Therefore, Ravind's luggage charge = 2fk
But, fk = 400. Therefore, Ravind's luggage charge = Rs. 800.
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36. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
Answer:
Explanation:If one letter is in wrong envelope, one other letter must also be in wrong envelope. So zero is the probability that exactly 1 letter is inserted in an improper envelope.
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37. In the year 2002, Britain was reported to have had 4.3m closed-circuit televisions (CCTV) cameras - one for every 14 people in the country. This scrutiny is supposed to deter and detect crime. In one criminal case, the police interrogates two suspects. The ratio between the ages of the suspects is 6:5 and the sum of their ages is 66 years. After how many years will the ratio be 8:7?
Answer:
Explanation:A/6 =B/5=x;
A=6x;B=5x;
A+B=66; ==> x=6;
A=36, B=30;
After X years,((A+X)/(B+X))=(8/7)
Solve the above eqn, we get X=12.
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38. Anoop managed to draw 6 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side. Find the ratio of the side of the square to the
radius of the circles. Assume √2 is 1.4.
Answer:
Explanation:Let the radius of circle be r Let the side of square be a
Then diagonal of square= a*sqrt(2)
This diagonal length = 12*r + 2r * sqrt(2)
(Because the extreme circle's radius is perpendicular to side of square.)
Thus we get 12*r+2r*sqrt(2)=a*sqrt(2) r (6*sqrt(2)+2)=a r/a=1/(6*sqrt(2)+2)
Thus ratio: r: a = 1 :( 6*sqrt(2)+2)
= 1: 10.4
So, a : r = 10.4 : 1
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39. Alok and Bhanu play the following min-max game. Given the expression N = 9 + X + Y - Z, where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game would be
Answer:
Explanation:Actually only Alok chooses numbers. So he wants to maximize the numbers.
Since there are two positive and one negative sign, he will definitely choose 9 so as to get the maximum value.
Since maximum of x+y-z can be obtained only from that way
So 9+9+9-9 = 18.
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40. If a pipe can fill the tank in 6 hrs but unfortunately there was a leak in the tank due to which it took 30 more minutes .Now if the tank was full how much time will it take to get emptied through the leak?
Answer:
Explanation:Work done by the leak in 1 hour = [(1/6)-(2/13)]=1/78 hrs.
Time taken= 78 hrs
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