The voice of a woman is sharper than man because :

Solution
The pitch of woman's voice is more
Statement I : No pennission is guaranteed for discussion on any secret proposal.
Statement II : There was no secret proposal last week.
Concluasion : It was discussed by the concerned parties.

Solution
It is definitely true
The diagonals of a rhombus are 30cm and 40 cm long. Find its side.

Solution
Side =^{1}⁄_{2} \(\sqrt{d_{1}^{2}+d_{2}^{2}}\)
= \(\frac{1}{2}\sqrt{(30)^{2}+(40)^{2}}\)
=\(\frac{1}{2}\sqrt{900+1600}=\frac{1}{2}\sqrt{2500}\)
=^{1}⁄_{2}×50= 25 cm
Directions: In the following bar diagrwn the production of wheat. rice and other food grains in four States P. Q. R and S has been represented. Study the following diagram carefully and answer the questions :
Ramesh has some cows and hens. If the number of total heads be 48 and that of legs be 140, then find the number of hens.

Solution
Let the number of cows be x
and that of hens be y Then,
x+ y = 48.....(i)
4x + 2y = 140......(ii)
Putting x = 48  Y in equation (ii).
4(48  y) + 2y =140
⇒ 192  4y +2y =140
⇒ 2y = 52
⇒ Y = 26
Directions: In the following bar diagrwn the production of wheat. rice and other food grains in four States P. Q. R and S has been represented. Study the following diagram carefully and answer the questions :
Each edge of a cube is increased ‘by 50%. What will be the per cent increase in its volume?

Solution
Let the edge of the cube be x cm.
Increased length =^{3}⁄_{2}x cm
Original volume = x^{3}
New volume = ^{27}⁄_{8} x^{3}
Increase =^{27}⁄_{8} x^{3}x^{3}=^{19}⁄_{8}x^{3}Percentage increase=\(\frac{19}{x^{3}}x^{3}\times 100= 237.5%\)
Directions: In the following bar diagrwn the production of wheat. rice and other food grains in four States P. Q. R and S has been represented. Study the following diagram carefully and answer the questions :
What per cent of total production of other food grains is produced by State R?

Solution
Total production of other food grams = 20+50+70+90
= 230 tonnes
Required percentage = ^{70}⁄_{230} ×100
= 30.4%
Directions: In the following bar diagrwn the production of wheat. rice and other food grains in four States P. Q. R and S has been represented. Study the following diagram carefully and answer the questions :
What per cent of total production of wheat is produced by State P ?

Solution
Total production of wheat
= 315 tonnes
Production by State P = 80 tonnes
Required percentage
= ^{80}⁄_{315} ×100 = 25.4%
Directions: In the following bar diagrwn the production of wheat. rice and other food grains in four States P. Q. R and S has been represented. Study the following diagram carefully and answer the questions :
What is average production if wheat in all States taken together?(in tonnes)

Solution
Average production of wheat\(\frac{80 + 95 + 60 + 80}{4}=\frac{315}{4}= 78.75 \: tonnes\)
Directions: In the following bar diagrwn the production of wheat. rice and other food grains in four States P. Q. R and S has been represented. Study the following diagram carefully and answer the questions :
Which State is the largest producer of wheat?

Solution
Production ofWheat by
by P = 150  70 = 80 Tonnes
Q = 225  130 = 95 Tonnes
R = 200  140 = 60 Tonnes
S = 270  190 = 80 Tonnes
So largest producer of wheat= Q state
Directions: In the following bar diagrwn the production of wheat. rice and other food grains in four States P. Q. R and S has been represented. Study the following diagram carefully and answer the questions :
What Percentage of rice is produced by State S out of total production of rice ?

Solution
Total production of rice
= 50+80+70+100= 300 tonnes Production by State S
= 100 tonnes
∴ 'Required percentage
= \(\frac{100}{300}\)×100 = 33.3%