Solution:
Number of rolls sold by noon = $$\frac{1}{2}$$ of 40 dozen = 20 dozen
Number of rolls sold between noon and closing time :
= 60% of 20 dozen
= $$\left( {\frac{{60}}{{100}} \times 20} \right)$$   dozen
= 12 dozen
Number of rolls left unsold :
= [40 - (20 + 12)] dozen
= 8 dozen

Solution:
Let the third number be $$x$$
Then, first number :
= $$112\frac{1}{2}\% $$  of $$x$$
= $$\frac{9x}{8}$$
Second number :
= 125% of $$x$$
= $$\frac{5x}{4}$$
∴ Required percentage :
= $$\left( {\frac{{9x}}{8} \times \frac{{4}}{{5x}} \times 100} \right)$$   %
= 90%

Solution:
If we take different values of x then,
Let x = 150, then error%
$$\eqalign{ = \frac{{ {\frac{{ {200 - 100} }}{{100}}} }}{{100}} \cr = 100\% \cr} $$
Again if x = 100, then error%
$$\eqalign{ = \frac{{ {\left( {150 - 50} \right) \times 100} }}{{100}} \cr = 200\% \cr} $$
If we take different value of x,
we get different answer so we can't determine it.

Solution:
(a) x% of y = $$\frac{xy}{100}$$ and y of z = $$\frac{yz}{100}$$
x > y, y < z
⇒ xy > yz
⇒ $$\frac{xy}{100}$$ > $$\frac{yz}{100}$$
⇒ x% of y > y% of z

(b) y% of x = $$\frac{xy}{100}$$ and z% of y = $$\frac{yz}{100}$$
As proved above, y% of x > z% of y

(c) z% of x = $$\frac{xy}{100}$$ and y% of z = $$\frac{yz}{100}$$
x > y
⇒ xz > yz
⇒ $$\frac{xz}{100}$$ > $$\frac{yz}{100}$$
⇒ z% of x > y% of z

Solution:
Minimum pass percentage for Boys = 60% A boy gets 767 and failed by 313, it means 767 + 313 = 60% 1080 = 60% 60% = 1080 Or, 1% = $$\frac{{1080}}{{60}}$$ Or, 45% = $$\frac{{1080 \times 45}}{{60}}$$   = 810 So minimum passing marks for girls = 810

Solution:
10% = $$\frac{1}{10}$$
\[\begin{gathered} {\text{Initial }}\,\,\,\,\,\,{\text{Final}} \hfill \\ \,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,9 \hfill \\ \,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,9 \hfill \\ \overline {\,\,100\,\,\,\,\,\,\,\,\,\,\,\,\,81\,\,\,} \hfill \\ \end{gathered} \]
⇒ 81 units = Rs. 8100
⇒ 1 unit = Rs. 100
⇒ 100 units = Rs. 10000
⇒ Value of property 2 years ago
⇒ Rs. 10000

Solution:
Cost of fresh mangoes + Cost of packaging = Total cost Let initial Cost of fresh, mangoes = 100 Then, packaging cost = 40 Thus, Initial total cost = 100 + 40 = 140 After increasing in cost of fresh mangoes 30%, Cost of fresh mangoes = 130 And cost of packing go down by 50 % so, Cost of packing = 20 Now Total cost = 130 + 20 = 150 Increased cost = 150 - 140 = 10 % increased = $$ = \frac{{10 \times 100}}{{140}} = 7.14\% $$