Percentage - 04

Explanation:-

$$\eqalign{ & {\text{Let the positive number be x}}. \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr & x \times x = x + \frac{{\left( {x \times 2000} \right)}}{{100}} \cr & {x^2} = x + 20x \cr & {x^2} - 21x = 0 \cr & {\text{Either}}, \cr & x = 0,\,\,or \cr & x = 21 \cr & {\text{21}}\,{\text{is}}\,{\text{the}}\,{\text{possible}}\,{\text{value}}{\text{.}} \cr & {\text{Then}}\,{\text{square}}\,{\text{of}}\,21\,{\text{is}}\,441. \cr}$$

Explanation:-

Non-defective products M¹ = 25 X 0.98 = 24.5%
Non-defective products M² = 35 X 0.96 = 33.6%
Non-defective products M³= 40 X 0.95 = 38%
Percentage of non-defective products = 24.5 + 33.6 + 38 = 96.1%

Explanation:-

100 ==25% ↑ ==> 125 ==x%↓ ==> 100.
x% = (25 *100) /100 = 20%.
We don't need the actual value to calculate the answer.

Explanation:-

Female employees = 45%
Male employees = 55%
Difference = 55 - 45 = 10%
→ 10% = 72
→ 1% = 72 /10
→ 100 = 7.2 * 100 = 720.

Explanation:-

Let the number of people be x who has been asked for the donations.
People already solicited = 60% of x = 0.6x
Remaining people = 40% of x = 0.4x
Amount collected from the people solicited,
= 600 *0.6x = 360x
360x = 75% of the amount collected.
Remaining amount = 25% = 120x
Thus,
Average donations from remaining people,
= 120x /0.4x = 300.

Explanation:-

$$\eqalign{ & {\text{Actual}}\,{\text{result}} = 10x \cr & {\text{By}}\,{\text{mistake}}\,{\text{it}}\,{\text{has}}\,{\text{been}}\,{\text{divided}}\,{\text{by}} \cr & 10 = \frac{x}{{10}} \cr & \% \,{\text{change}} = \left[ {\frac{{10x - \left( {\frac{{10}}{x}} \right)}}{{10x}}} \right] \times 100 = 99 \cr & = - 99\% \cr & {\text{Since, actual value is greater than the wrong value}}{\text{.}} \cr & \cr & {\text{Alternatively,}} \cr & {\text{Let}},\,x = 10 \cr & {\text{Actual}}\,{\text{result}} = 10 \times 10 = 100 \cr & {\text{Wrong}}\,{\text{result}} = \frac{{10}}{{10}} = 1 \cr & {\text{Change}} = \left( {1 - 100} \right) = - 99 \cr & \% \,{\text{change}} = - 99\% \cr}$$

Explanation:-

Copper : Aluminum = 7 : 4.
Let Copper and Aluminum in the weapon be 7x and 4x respectively.
Given,
Aluminum in weapon = 12 kg
So,
→ 4x = 12.
→ x = 3
Copper = 7x = 7 * 3 = 21 Kg.
Total alloy in the weapon = 12 + 21 = 33 kg
But 12% alloy get destroyed in making the weapon, i.e. 88% alloy is used in the weapon, so,
→ 88 % alloy = 33 kg
→ 100 % alloy = 37.5 kg.

Explanation:-

Result	Physics	Chemistry
Failed	35%	45%
Passed	65%	55%

Now, 55% of 600 passed in Chemistry = (55 X 600) / 100 = 330 From question, 40% of those who passed in Chemistry(330 Students) also passed in physics => (40 X 330) / 100 = 132 ,
so, 132 students passed in both
Therefore % who passed in both = (132 X 100 ) / 600 = 22%
Passed in both subject = 22% of total students
% of students who passed in either Physics or Chemistry or both,
= (65 +55) -22 = 98%
Thus, percentage of students who failed in both subjects,
= 2%
Number of students who failed = 2% of 600 = 12.

Explanation:-

Let the initial revenue be 100.
100 ----- 50% ↑ (Ticket up)-----> 150 ----- 20% ↓ (Visitors down) -----> 120.
There is 20% increase in the revenue.

Explanation:-

$$\eqalign{ & {\text{Daily}}\,{\text{supply}}, \cr & = \left( {100 - z} \right)\% \,{\text{of}}\,y \cr & = \frac{{\left\{ {\left( {100 - z} \right)y} \right\}}}{{100}} \cr & {\text{Thus,}}\,{\text{required}}\,{\text{number}}\,{\text{of}}\,{\text{days}} \cr & = \left[ {\frac{{\left( {100x} \right)}}{{\left( {100 - z} \right)y}}} \right] \cr}$$