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A father said to his son, " I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was:
Let the son's age 5 years back be x.
∴ Present age of son = x + 5
∴ 38  (x + 5) = (x + 5)
or 38  5  5 = 2x
or x = 28/2 = 14 years
The area of a rectangle is 4 times the area of a square. The length of the rectangle is 90 cms and the breadth of the rectangle is 2/3 of the side of the square. What is the side of the square?
Let the side of the square = x cm
Then breadth of the rectangle = 2/3 x
∴ Area of rectangle = (90 x 2/3 x) cm^{2}
= 60 x cm^{2}
∵ 60 x = 4x^{2}
⇒ x = 15 cm
So the side of the square = 15 cm
Which is the number that comes next in the sequence :
0, 6, 24, 60, 120, 210 ?
0, 6, 24, 60, 120, 210, ?
1 x 2 x 3 = 6
2 x 3 x 4 = 24
3 x 4 x 5 = 60
4 x 5 x 6 = 120
5 x 6 x 7 = 210
6 x 7 x 8 = 336
20 litres of a mixture contains 20% alcohol and the rest water. If 5 litres of water be mixed in it, the percentage of alcohol in the new mixture will be
Initially, the mixture contains 4 litres of alcohol and 16 litres of water
Then the mixture contains 4 litres of alcohol and 21 litres of water
∴ Percentage of alcohol = ( 4/25 x 100) = 16%
Two trains each 120 metres in length, run in opposite directions with velocities of 40 m/sec and 20 m/sec respectively. How long will it take for the tail end of the two trains to meet each other from the time their engines crossed each other?
Relative speed = (40 + 20) m/s
= 60 m/s
Distance covered = (120 + 120)m = 240 m
∴ Required Time = 240 x 1/60 = 4 sec
The simple interest on a certain principal at the rate of 9.5% pa is Rs 950 for 2 yrs. How much will be the additional interest on the same amount for the same period at the rate of 10.5% per annum?
Simple interest = PRT/100
950 = P x 9.5 x 2/100
⇒ 19P = 95000
⇒ P = 95000/19 = 5000
New SI at the rate of 10.5% per annum
SI = PRT/100 = 5000 x 10.5 x 2/100 = 1050
Difference = 1050  950 = Rs 100
A circus tent is cylindrical up to a height of 5m and conical above it. If its diamter is 105 m and slant height of the conical portion is 53 m. The area of the canvas used to build the tent is
Given height of cylinder (h) = 5m
Deameter of conical part d = 105m
So, radius of conical part (r) = radius of cylindrical part (r) = 52.5m
Slant height of conical portion (l) = 53m
Area of canvas required = CSA of cylindrical part + CSA of conical part
Each of the following questions consists of two sets of figures. Figures 1,2,3 and 4 constitute the Problem Set while figures A,B,C,D and E constitute the Answer Set. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the Answer Set .
In the following problem, out of the five figures marked 1, 2, 3, 4, and 5, four are similar in a certain manner. However one figure is not like the other four. Choose the figure which is different from the rest.
Only if fig. (4), all the leaves have their outer halves shaded.
In the following questions, select a figure from amongst the four alternatives, which when placed in the blank space of fig. (X) would complete the pattern.
Ten members I, J, K, L, M, N, O, P, Q and R are split into two teams X and Y of 5 members each. Members in the two teams are made to sit in two rows facing each other in such a way that one member of team X is sitting exactly opposite of a member in team Y. Members of team X are facing North. L is third to the right of I and sits exactly opposite of O. J sits to the immediate right of O and is facing South. P is third to the right of J and is exactly opposite of N. K sits between I and M and is opposite of Q.
Q. Who is second to the left of K?
(a) A cube has six sides, each of which has a different colour:
black, blue, brown, green, red and white.
(b) The red side is opposite the black.
(c) The green side is between the red and the black.
(d) The blue side is adjacent to the white.
(e) The brown side is adjacent to the blue.
(f) The red side is the bottom face.
Q. The four colours adjacent to green are:
In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4 : 3. It is also known that the length of PO is 28 cm.
Q. What is the ratio of the length of PQ to that of QO ?
In each of the following letter series, some of the letters are missing which are given in that order as one of the alternatives below it. Choose the correct alternative.
Q. f _ h i g h _ j h i j _ i j _ l _ k l m
In each of the following questions, the two expressions on either side of the sign (=) will have the same value if two terms on either side or the same side are interchanged. The correct terms to be interchanged have been given as one of the five alternatives under the expressions. Find the corect alternative in each case.
Q. 5 + 3 × 6  4 ÷ 2 = 4 × 3  10 ÷ 2 + 7
On interchanging 6 and 4 on L.H.S., we get the statement as:
5 + 3 × 4  6 ÷ 2 = 4 × 3  10 ÷ 2 + 7
or 5 + 12  3 = 12  5 + 7
or 14 = 14, which is true
Below are the statements followed by two conclusions numbered I and II. You have to consider the statements and the following conclusions and decide which of the conclusion(s) follows the statement(s).
Statements :
a. All books are pens.
b. All pens are pencils.
Conclusions:
I. All books are pencils.
II. All pencils are books.
The following table gives Population and Activities of Indian Children (199394). Study the table carefully and answer these questions.
Q. What is the average of Rural Males Population in millions?
Average of rural male population
The following table gives Population and Activities of Indian Children (199394). Study the table carefully and answer these questions.
Q. In which category of population, there is the lowest percentage of children in the school?
The following table gives Population and Activities of Indian Children (199394). Study the table carefully and answer these questions.
Q. What is the approximate percentage of children of all categories not in school?
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