Question 1
In a journey, Lakshmi travels 150 km by bus, 240 km by car and 80 km by boat. The speed of bus is 5 times the speed of boat and the speed of car is 6 times the speed of boat. If Lakshmi took 15 hours to travel altogether, what is the speed of boat in kmph?
(A) 10
(B) 15
(C) 20
(D) 25
Question 2
Ramesh has a number of bags into which he can put rupees in whole number quantities. What is the minimum number of bags Ramesh would require so that he can select any amount of rupees between 1 and 25 by simply taking bags together?
(A) 3
(B) 4
(C) 5
(D) 25
Question 3
In a class, 55% of the students are boys. During a special class, 60% of the girls were present. If all the students present for the special class was 75% of the total number, what percent of boys from the class were there for the special class?
(A) 57
(B) 67
(C) 77
(D) 87
Question 4
Consider the following figures:
Which of the following numbers should be put in place of the question mark?
(A) 5
(B) 7
(C) 9
(D) 11
Question 5
Pointing to a woman, a man said “Her mother is the only daughter of my mother”. How is the woman related to the man?
(A) Sister
(B) Daughter
(C) Niece
(D) Mother
N.B. Please note that the official timings for publication of these questions is 11 am daily.
SOLUTIONS TO DAILY CSAT MISSION #99
1. (B) 2. (B) 3. (A) 4. (C) 5. (A)
Explanations
1. Simple enough question. When he gives he gives away one-fourth, he has three-fourths of the original amount remaining with him. Then after he gives away one-third, he has two-thirds of that three-fourth amount with him. If he had M amount originally, then money left with him is 2/3 x 3/4 x M. This is given as 40. So, M is 80.
Alternately, you can use percentages to solve this. If he had 100% of the amount at the beginning, he has 75% of the amount after giving away to Vinod, and two-thirds of this 75% i.e. 50% (2/3 x 75) at the end. Now if 50% of the original amount is 40 (as given in question), then 100% of the original amount is 80.
2. Let his average after 16 innings be ‘x’. So total number of runs scored by him after 16 innings is 16x.
Average after 17 innings is x+3 as per the question. So total number of runs after 17 innings is 17(x+3).
Now total runs after 17 innings = Total runs after 16 innings + runs scored in 17th innings.
So, 17(x+3) = 16x + 85 which gives x to be 34. So, x+3 is 37.
3. Since it will take 4 minutes to rescue the people, the vessel only has 16 minutes to reach the ship before it sinks completely. 16 minutes = 16/60 hours. Distance : 12 km. So, net relative speed of vessel and ship has to be Distance/Time i.e. 12/(16/60) = 45 kmph. Speed of ship is 8, so speed of vessel has to be 45-8 = 37 kmph.
4. This is one of the kind of questions that UPSC asks to waste your time in the exam. If you know the trick, then it’s easy. If you dont, you will probably get lost because there will be like 6 zeroes in the equation while converting 6400 km into metres. Here’s the trick:
Circumference of thread initially : 2 x 22/7 x 6400. ( Don’t calculate the actual value, keep this as 2 x 22/7 x 6400).
Circumference of thread after it expands : 2 x 22/7 x (6400+s) where s is taken as the increase in the radius.
It is given that final circumference is 10 more than the initial circumference. So :
[2 x 22/7 x (6400+s)] – [2 x 22/7 x 6400] = 10 which gives a simple equation : 2 x 22/7 x s = 10, which gives s as 1.6 metres.
5. Let the total journey be ‘x’ km. So, the distance covered in third part of journey is calculated to be x – x/3 – x/4 = 5x/12.
Time taken to complete first part of journey : Distance/Speed = (x/3)/25 = x/75.
Time taken to complete second part of journey : Distance/Speed = (x/4)/30 = x/120.
Time taken to complete third part of journey : Distance/Speed = (5x/12)/50 = x/120.
So, total time taken = x/75 + x/120 + x/120 = 3x/100.
Therefore, average speed over the journey = Total distance covered/ Total time taken = x/(3x/100) = 100/3 = 33.
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