The average age of a man and his son is 33 years. The ratio of their ages is 8 : 3 respectively. What is the man's age?
Total age of the father and the son
= 2 x 33
= 66 years
Ratio in Father's age and son's age
= 8 : 3
∴ Father's age = 8 x 66/8 + 3
= 48 years
If x + y = 6 and 3x  y = 4, then x  y is equal to
x + y = 6
⇒ y = 6  x
Now, 3x  y = 4
or 3x  (6  x) = 4
or 3x  6 + x = 4
or 4x = 10
or x = 5/2
∴ y = 6  5/2 = 7/2
∴ x  y = 5/2  7/2 = 1
The area of the circumcircle of the equilateral triangle whose one side lies on the diagonal of a square with side 4 cm is (use π = 3.14)
Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expenses per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?
Let x be the fixed cost and y the variable cost
17500 = x + 25y .....(i)
30000 = x + 50y .....(ii)
Solving the equation (i) and (ii), we get
X = 5000, y = 50
Now if the average expense of 100 boarders be 'A'
Then 100 x A = 5000 + 500 x 100 ⇒ A = 550
In what time will Rs. 500 give Rs. 50 as interest at the rate of 5% per annum simple interest?
SI = 50
P = 500
R = 5% pa.
SI = P x R x T/100
⇒ 50 = 50 x 5 x T/100
⇒ T = 2 years
select the correct combination of mathematical signs to replace * sign to balance the given equation.
1*111*111*12321
1 × 111 × 111 = 111 × 111 = 12321
One pipe can fill a tank 3 times as fast as another pipe. If the 2 pipes together can fill the tank in 36 minutes, the slower pipe alone will be able to fill the tank in
Let the slower pipe alone fill the tank in x minutes
Then, faster pipe will fill in x/3 minutes
∴ 1/x + 3/x = 1/36
⇒ 4/x = 1/36
⇒ x = 144 min
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is :
Speed = (45 x 5/18 )m/sec = ( 25/2 )m/sed
Time = 30 sec
Let the length of bridge be x metres
Then, 130 + x/30 = 25/2
⇒ 2(130 + x) = 750
⇒ x = 245m
By selling an article at 2/5 of the marked price, there is a loss of 25%. The ratio of the marked price and the cost price of the article is:
999 x 99 x 9 = ?
7 is added to a certain number; the sum is multiplied by 5; the product is divided by 9 and 3 is subtracted from the quotient. the remainder left is 12. The number is :
Let the number be x Then
5(x + 7)/9  3 = 12
⇒ 5(x + 7)  27 = 108
⇒ 5x + 35 = 135
⇒ 5x = 100
⇒ x = 20
If cos (θα)=a and sin (θβ)=b, then cos^{2}(αβ)+2 ab sin (αβ) is equal to
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 .
The central element is enlarged and the number of sides in this elements increases by one. The upper element rotates 90° CW and is placed on the RHS inside the enlarged element. The lower element rotates 90° ACW and is placed on the LHS inside the enlarged element.
In the following problems, 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.
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.
Consider three circular parks of equal size with centers at A_{1}, A_{2}, and A_{3} respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A_{1}A_{2}A_{3}, B_{1}B_{2}B_{3} and C_{1}C_{2}C_{3} as shown. Three sprinters A, B and C begin running from points A_{1}, B_{1} and C_{1}respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point.
Q. Let the radius of each circular park be r, and the distances to be traversed by the sprinters A, B and C be a, b and c, respectively. Which of the following is true?
⇒ Distance travelled by A = a = 3 × 2r = 6r.
ΔA_{1}B_{1}D is a 30°, 60°, 90° triangle.
So, B_{1}D = √3r/2
⇒ B_{1}B_{2} = 2r + 2 × √3r/2 = r (2 + √33)
⇒ Distance travelled by B
= b = 3 × r (2 + √3) = 3r (2 + √3)
ΔA_{1}C_{1}E is a 30°, 60°, 90° triangle.
So, C_{1}E = √33r.
⇒ C_{1}C_{2} = 2√3 r + 2 r = 2r (1 + √3)
⇒ Distance travelled by C = c = 3 × 2r (1 + √3) = 6r (1 + √3)
Now, b  a = 3√33r and c  b = 3√3r.
With the help of the given diagram, answer the following questions making the right choice from the given alternatives. Indicate the answer as per the "Instructions"
Q. Qualified and experienced doctors working in villages are represented by the letter .....
In each of the questions below are three statements followed by three conclusions numbered I, II and III. You have to consider the statements and the following conclusions and decide which of the conclusions is logically follows from the given statements.
Q.
Statements:
a. All pins are rods.
b. Some rods are chains.
c. All chains are hammers.
Conclusions:
I. Some pins are hammers.
II. Some hammers are rods.
III. No pin is hammer.
Use the following table to answer the following questions.
Q. How fast was the train moving 2 1/2 hours after the timed period?
Use the following table to answer the following questions.
Q. During the 3 hours shown in the table, the speed of the train increased by :
Use the following table to answer the following questions.
Q. At time t, measured in minutes, after the beginning of the time period which of the following gives the speed of the train in accordance with the table?







