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332 Aptitude Questions And Answers

163⟩ Ten boxes are there. Each ball weighs 100 gms. One ball is weighing 90 gms. i) If there are 3 balls (n=3) in each box, how many times will it take to find 90 gms ball? ii) Same question with n=10 iii) Same question with n=9

If n=3 then answer is:1

Take two balls and weigh. If both are equal then remaning ball is 90 gms

else if second is less than first one then second ball is 90gms

else if first is less than second on then first ball is 90 gms

If n=10 answer is: 3

Divide the n=10 into two 5-sub groups

compare the both the groups

If 1group<2group then 90 gms ball is present in the first group

else it is present in the second group.

Take the less weight group and divide it into 2-2-1 subgroup.

Now compare the 2-subgroups first. If first 2-subgroup is less than the second 2-subgroup then 90gms is present in the first 2-subgroup otherwise it is present in the second 2-subgroup. If both are equal then the remaing 1-subgroup ball is 90gms ball.

Now take less weigth subgroup of 2-subgroups. Now compare the two balls that are existing in the 2-subgroup group. Then we can find the 90 gms ball.

So we require 3 chances for detection of 90 gms ball when n=10

If n=9 then answer is :3

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164⟩ There are two square rooms. Both are of same height. The second room is 5m longer than the first room. The rate for papering the walls is 10 paisa per square meter. The total cost for papering the rooms is Rs 60 and Rs 80. What is the height of the rooms?

A house will have four walls...

papers used only for construction of walls!!!!

1st House: 4 *a (side) *h (height) * 10 = 60 =======> 4ah=6 --(1)

Given 10 paise reqd...per construction of 1 square meters

2nd House: 4*(a+5) (side)*h (height) * 10 = 80 =======> 4ah + 20h=8---(2)

Area formula will be horizontal side*vertical height

the plane of wall will be along it's height!..

Solving (1) & (2) we get 20h=2.

Hence, h=0.1m

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167⟩ What is the sum of all the four digit numbers formed using the digits 0, 1, 2 and 3. None of the two digits should be repeated?

Process of solving

From these four digits '0' cannot be at first place to form four digit number

so we have 1, 2, or 3 can be at thousand's place

keeping one digit at thousand place can have 6 different four digit number

so that means

1000*6 + 2000* 6 + 3000* 6 = 36000

Now come to hundred's place we can have all four digit at this place , '0' will not contribute any thing to sum so in all four digits number 1,2,3 will be at 4 times on same place

so that means

100*4 + 200* 4 + 300 * 4= 2400

Now come to tenth's place ...same as hundred

so

10*4 + 20*4 + 30*4= 240

same for unit place

1*4 + 2*4 + 3*4= 24

in last if you add whole the total sum of all possible four digit number formed is 38664

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168⟩ A tree grows only 3/5 as fast as the one beside it. In four years the combined growth of the two trees is eight feet.How much does the shorter tree grow in two years?(a) Less than 2 feet (b) 2feet (c) 2 1/2 feet(d) 3 feet (e) more than 3 feet.

even after 4 years the ratio remains d same..therefore:

x+(3/5)x=8

thus x=5

therefore the height of the shorter tree is 3 feet after FOUR years..

therefore after TWO years the heght will be 1.5 ft..

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175⟩ Paul, the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in 2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the group. The top two teams from each group enter the semi finals (after which the winner is decided by knockout).However, Paul has a soft spot for India and when India plays any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world cup?

We have two chances to win the world cup.

Either India can win all 10matches or Win 7 out of 8 group matches + win the semi final and final matches.

Case 1: To win all 10, probability is (2/3)^10.

Case 2: Probability of winning 7mathces out of 8= (2/3)^7 and

Probability of Loosing the 1 match= 1/3.

This process can occur in 8 ways.

probability= 8*((2/3)^7 * 1/3)

To win semi final and final match probability is (2/3)^2

Total probability=8*((2/3)^7 * 1/3) * (2/3)^2 = 8/3 * (2/3)^9.

So total probability, Case1+Case 2= (2/3)^10 + 8/3 * (2/3)^9

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178⟩ Falling height is proportional to square of the time. One object falls 64cm in 2sec than in 6sec from how much height the object will fall?

The falling height is proportional to the squere of the time.

Now,the falling height is 64cm at 2sec

so, the proportional constant is=64/(2*2)=16;

so, at 6sec the object fall maximum (16*6*6)cm=576cm;

Now, the object may be situated at any where .

if it is>576 only that time the object falling 576cm within 6sec .Otherwise if it is situated<576 then it fall only that height at 6sec.

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