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The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is
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Explanatory Answer
Let Narayanan take X hrs to reach B then Partha would take X + 4 hrs
Its given that Partha reaches the mid-point of A and B two hours before Narayan reaches B
X+4 / 2 = X – 2 => X=8 hrs
So, Partha would take 8+4 = 12 hrs to travel 60 Kms at a speed of 60/12 Kmph
Speed of Partha = 5 Kmph
If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals.
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In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is
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Explanatory Answer
Given ∠AOB = 60°
Area of Sector AOB = 60/360 × π = π/6 ---(1)
Given OC = OD => ∠OCD = ∠ODC = 60°
△OCD is an Equilateral Triangle with side = a
Area(△OCD) = √3/4 × a × a ---(2)
Its given that Area(OCD) = 1/2 × Area(OAB)
a 2 (√3/4) = π / ( 6×2)
a = (π/ 3√3) 1/2
A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is
Video Explanation
Explanatory Answer
Given, The amount of B in mixture ≤ Amount of A in mixture
Selling Price = Rs. 264 and Profit = 10 %
264 = 1.1 × CP
CP = 264/1.1 = Rs. 240 for 10 litres
CP per litre = Rs. 24
We also know that, CP per litre of A = CP per litre of B + 8 Let CP per litre of B = x So, CP per
litre of A = x + 8
Given Amount of B ≤ Amount of A,
Maximum possible cost of B occurs when B = A
We need to choose values for A and B in such a way that the quantities remain same.But A should
be 8 more than B
Therefore, A should have a CP per litre of Rs. 28 and B should have a CP per litre of Rs 20
B cannot be assigned any more than this as the amount of B would become more than A
Example: Let us assign B to be Rs. 21 and A to be Rs. 29 which would result in a ratio of 3:5 where
B amounts more than A, which doesn’t satisfy the condition
Max possible cost of Paint B = Rs. 20 per litre
Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.
Based on the given information, which of the following statements MUST be FALSE?
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What is the number of bureaucrats in the administration committee? (TITA)
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What is the number of educationalists in the research committee? (TITA)
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Which of the following CANNOT be determined uniquely based on the given information?
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Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes - X, Y, and Z. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects. The following facts are known about the eight students:
1. Three students are from X, three are from Y, and the remaining two students, both female, are from Z.
2. Both the male students from Y minor in Finance, while the female student from Y majors in Operations.
3. Only one male student majors in Operations, while three female students minor in Marketing.
4. One female and two male students major in Finance.
5. Adriana and Deb are from the same institute. Daisy and Amit are from the same institute.
6. Barun is from Y and majors in Operations. Chetan is from X and majors in Finance.
7. Daisy minors in Operations.
Who are the students from the institute Z?
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Which subject does Deb minor in?
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Which subject does Amit major in?
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If Chitra majors in Finance, which subject does Bandita major in?
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Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.
1. Contamination levels at three pumps among P1 – P5 were recorded as high.
2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low.
3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps P16 – P20.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.
Which of the following MUST be true?
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What best can be said about the number of pumps at which the contamination levels were recorded as medium?
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If the contamination level at P11 was recorded as low, then which of the following MUST be true?
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If contamination level at P15 was recorded as medium, then which of the following MUST be FALSE?
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An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.
In how many different ways can the ATM serve a customer who gives 500 rupee notes as her preference? (TITA)
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If the ATM could serve only 10 customers with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, what is the maximum number of customers among these 10 who could have given 500 rupee notes as their preferences? (TITA)
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What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?
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What is the number of 500 rupee notes required to serve 50 customers with 500 rupee notes as their preferences and another 50 customers with 100 rupee notes as their preferences, if the total number of notes to be dispensed is the smallest possible?
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What is the percentage increase in sales in December 2017 as compared to the sales in December 2016?
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In which quarter of 2017 was the percentage increase in sales from the same quarter of 2016 the highest?
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During which quarter was the percentage decrease in sales from the previous quarter’s sales the highest?
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During which month was the percentage increase in sales from the previous month’s sales the highest?
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You are given an n×n square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.
What is the minimum number of different numerals needed to fill a 3×3 square matrix? (TITA)
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What is the minimum number of different numerals needed to fill a 5×5 square matrix? (TITA)
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Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?
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Suppose that all the cells adjacent to any particular cell must have different numerals. What is the minimum number of different numerals needed to fill a 5×5 square matrix?
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