In a joint family the average age of grand parents is 67 years, the average age of parents is 35 years and that of three grand children is 6 years. What is the average age of family?

Solution
Average age of family
\(=\left ( \frac{2\times 67 + 2 \times 35+ 3\times 6)}{7} \right )years\)
\(=\frac{134+70+18}{7}=\frac{222}{7}\)
\(=31\frac{5}{7}years\)
The length of a plot of land is four times its breadth. A playground measuring I, 200 m^{2} occupies one third of the total area of the plot.What is the length of the plot in metres?

Solution
Let the breadth of the plot be xm.
∴ Length = 4x m.
According to the question,
Area of the playground\(=\frac{1}{3}\times 4x\times x=\frac{4x^{2}}{3}m^{2}\)
\(\therefore \frac{4}{3}x^{2}=1200\Rightarrow x^{2}=\frac{1200 \times 3}{4}\)
\(\Rightarrow x^{2}=900m^{2}\)
\(\Rightarrow x=\sqrt{900}=30m\)
∴ Length of plot = 4x = 4 × 30 = 120m
The length of rectangle is increased by 40% and its breadth decreased by 30%. The change in the area of the rectangle is

Solution
If the length of a rectangle be increased by x% and its breadth be decreased by y% then effectiv change in its area
\(=\left ( xy\frac{xy}{100} \right )\)%
\(=\left ( 4030\frac{40\times 30}{100} \right )\)%
= (10  12)% = 2%
Negative sign shows decrease in area.
Two trains from Patna to Ranchirun at 6 pm and 6.30 pm and their speeds are 60 km/hour and 75km/hour respectively.After how many kilometres from Patna will both trains meet?

Solution
Distance covered by train 30 minutes moving at 60 kmph in
= 6O×^{1}⁄_{2}=30 km
Relative speed = (75  60) Kmph = 15kmph
Hence both trains will meet after ^{30}⁄_{15} = 2 hours.
∴Distance travelled by the train moving at 75 kmph in 2 hours
= 75 × 2 = 150 km
In an examination 65% students passed in Civics and 60% in History. 40% passed in both subjects.If 90 students failed in History and Civics both, what is the total number of students?

Solution
Let the number of students= 100
Number of students passing in
either civics or history or both
=65+6040=85
∴ Number of unsuccessful students= 15
∴ Required number of students
=^{100}⁄_{15}×90=600
The Panchayati Raj was first introduced in

Solution
1959
Who among the following received the Bharat Ratna award first ?

Solution
CVRaman
At which degree of scale the Farenheit and Celsius scale show the same temperature?

Solution
 40°
What is doldrum ?

Solution
Region of low pressure
Ozone layer is found in the range of

Solution
30 km to 50 km