April 30, 2021 - CSAT Quiz
1. John takes 15 hours to complete a certain job, while Basheer takes only 6 hours to complete the same job. If Stephen is faster than John but slower than Basheer at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?
(a) 2 hours, 30 minutes
(b) 2 hours, 45 minutes
(c) 3 hours, 20 minutes
(d) 3 hours, 45 minutes
2. Machine A takes 10 hours to complete a certain job and starts that job at 9AM. After one hour of working alone, machine A is joined by machine B and together they complete the job at 5PM. How long would it have taken machine B to complete the job if it had worked alone for the entire job?
(a) 15 hours
(b) 28 hours
(c) 20 hours
(d) 35 hours
3. A basket has 5 different fruits. A child is given the basket and he may pick out none, one or more of the fruits. In how many ways can this choice be made ?
(a) 16
(b) 8
(c) 32
(d) 64
4. The monthly incomes of X and Y are in the ratio of 4 : 3 and their monthly expenses are in the ratio of 3: 2. However, each saves Rs. 6,000 per month. What is their total monthly income?
(a) Rs. 28,000
(b) Rs. 42,000
(c) Rs. 56,000
(d) Rs. 84,000
5. Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling?
(a) 4
(b) 6
(c) 12
(d) 15
ANSWERS
1. Solution
Assume the units of work to be 90
Since John takes 15 hours to finish the work, the rate of John's work is 6 units/hour
Similarly, Basheer take 6 hours to finish the work, the rate of Basheer's work is 15 units/hour
Since it has been given that the rate of Stephen is greater than John and lesser than Basheer,
the range of Stephen's rate is between 6 units/hour and 15 units/hour
Hence the range of the time take to complete the work is between
90(6+6+15)90(6+6+15) = 3.33 hours(3 hour, 20 mins) - lower end
and 90(6+15+15)90(6+15+15) = 2.5 hours(2 hour, 30 mins) - higher end
only (b) is within this range
2. Solution
rate of A=1/10=7/70
rate of A+B=9/70
rate of B=2/70=1/35
B will complete job alone in 35 days
3. Solution
There are 2 ways to answer that question. There are 5 fruits in all and hence, 5 yes/no questions. Each set of answers [y n y n n], [y y n n n], etc represents a way of picking. In all the number of ways would be 2x2x2x2x2=2^5=32.
4. Solution
Let their incomes be 4x and 3x respectively and their savings be 3y and 2y respectively.
Thus savings of X and Y are respectively 4x – 3y and 3x – 2y.
Since both have same savings of Rs. 6000 per month that means : 4x – 3y = 3x – 2y, which means x = y.
Now saving of X = 4x-3y = 4x – 3x = x = Rs. 6000 (given).
Thus their total monthly income = 4x + 3x = 7 = Rs 42,000. Thus answer is option (b):
(b) Rs. 42,000
5. Solution
If the candidates can again use a bit of imagination they will realize that question is basically about finding the height of a cuboid whose length, breadth and the length of the diagonal joining opposite corners across the cuboid is given. The fly and point P are at the opposite corners across the cuboid in this case. We know that if a, b and c are length, breadth and height of a cuboid then the length of the diagonal, d, joining the opposite corners across the cuboid is equal to a²+b²+c² .
In this case, a = 8 m, b = 1 m, d = 9 m. Putting these values in above formula we get, c = 4 m. Thus the fly is 4 meters away from the ceiling. Therefore the answer is:
(a) 4
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