Percentage - Aptitude MCQ Questions and Solutions with Explanations

Let the fraction be $$\frac{{\text{x}}}{{\text{y}}}$$
When fraction is squared its numerator is reduced by $$33\frac{1}{3}$$ and denominator is reduced by 20%
$$\eqalign{ & {\text{According}}\,{\text{to}}\,{\text{question,}} \cr & {\left( {\frac{x}{y}} \right)^2} \times \frac{{33\left( {\frac{1}{3}} \right)\% }}{{20\% }} = 2\left( {\frac{x}{y}} \right) \cr & {\text{Or}},\,{\left( {\frac{x}{y}} \right)^2} \times \frac{{\left( {\frac{2}{3}} \right)}}{{\left( {\frac{1}{5}} \right)}} = 2\left( {\frac{x}{y}} \right) \cr & {\text{Or}},\,\frac{x}{y} = \frac{3}{5} \cr & {\text{Sum of numerator and denominator is}} \cr & \left( {x + y} \right) = 3 + 5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 8 \cr} $$

Let the percentage marks in QA =(10a + b)%
Let the percentage marks in DI = (10b + a)%
Let the percentage marks in VA = x%

Now, according to the question, we have,
$$\eqalign{ & \frac{{\left( {10{\text{a}} + {\text{b}}} \right) + {\text{x}} + \left( {10{\text{b}} + {\text{a}}} \right)}}{3} = {\text{x}} \cr & 11{\text{a}} + 11{\text{b}} + {\text{x}} = 3{\text{x}} \cr & {\text{or, x}} = \frac{{11\left( {{\text{a}} + {\text{b}}} \right)}}{2} \cr} $$
Clearly, we can see that the percentage of the VA section will be a multiple of 11
So, required answer will be 66

Let the initial price = Rs. 10000p
Price after first increment = 10000p + 100xp
Price after first decrement
= 10000p + 100xp - (100px + px²)
= 10000p - px²
Now, total decrement, px² = 21025 . . . . . (1)
Price after second increment,
= 10000p - px² + 100xp - $$\frac{{{\text{p}}{{\text{x}}^3}}}{{100}}$$
Price after second increment,
= 10000p - p² + 100xp - $$\frac{{{{\text{p}}^3}}}{{100}}$$ - 100xp + $$\frac{{{\text{p}}{{\text{x}}^3}}}{{100}}$$ - px² + $$\frac{{{\text{p}}{{\text{x}}^4}}}{{10000}}$$
= 10000p - 2px² + $$\frac{{{\text{p}}{{\text{x}}^2}}}{{10000}}$$
= 484416 . . . . . . (2)
On solving equation (1) and (2), We get
x = 20
Substituting back we get,
p = 5,25,625

No. of Machines	Output	Manuf. cost	Est. cost	Total cost	Profit
12	48, 000	24, 000	10, 000	34, 000	14, 000
11	44, 000	22, 000	10, 000	32, 000	12, 000

Profit,
= Output - total cost
= 44000 - 32000
= Rs. 12000
Initial value of share holders,
= 14000 $$ \times \frac{{10}}{{100}}$$
= Rs. 1400
New value of share holders,
= 12000 $$ \times \frac{{10}}{{100}}$$
= Rs. 1200
Decrease in Share holder value = 1400 - 1200 = 200
percentage decrease in the value of shareholders is :
$$\eqalign{ & = \frac{{200 \times 100}}{{1400}} \cr & = 14.28\% \cr} $$

Let the price of wheat is x per kg. Then price of wheat will be 5x per kg.
Expenditure on rice = 25 × x = 25x
Expenditure of wheat = 9 × 5x = 45x
Total cost,
25x + 45x = 350
70x = 350
x = 5
Hence, price of Rice = Rs. 5 per kg.
Price of wheat = 25 per kg.
Now, price of wheat = 25 ---- 20% ↑----> Rs. 30 per kg.
Let the new amount of rice is N kg, then
N*5 + 9*30 = 350
N = 16 kg.
% decrease in the amount of rice
$$\eqalign{ & = \frac{{\left( {25 - 16} \right) \times 100}}{{25}} \cr & = 36\% \cr} $$

Let the initial cost of raw material be 100. So, initial labor cost was 25 and net cost was 125
Now,
15% increment in raw materials cost and labor cost has gone up to 30% from 25 %
Raw material cost = 115 And
Labor cost = (115 × 30%) = 34.5
So, New net cost,
= 115 + 34.5 = 149.5
Difference of labor cost = 149.5 - 125 = 24.5
% reduction = $$\frac{{24.5 \times 100}}{{149.5}}$$   = 17%(approx.)

$$\eqalign{ & {\text{His bonus}}, \cr & = \frac{{ {20 \times 1000000} }}{{100}} \cr & = 2\, \text{lakh} \cr & {\text{Total}}\,{\text{profit}} = {\text{Net}}\,{\text{profit}} + \frac{{ {10 \times {\text{net}}\,{\text{profit}}} }}{{100}} \cr & 1.32\,\text{lakh} = {\text{Net}}\,{\text{profit}} \times \left[ {1 + {\frac{{10}}{{100}}} } \right] \cr & {\text{Net}}\,{\text{profit}} = \frac{{132000}}{{1.1}} = 120000 \cr & {\text{Commission}}, \cr & = \left( {{\text{Total}}\,{\text{profit}} - {\text{Net}}\,{\text{profit}}} \right) \cr & = 132000 - 120000 \cr & = 12000 \cr & {\text{Hence}}, {\text{his}}\,{\text{total}}\,{\text{earnings}} \cr & = 2\,\text{lakh} + 12000 \cr & = Rs.\,212000 \cr} $$

There is no need of the number of goats given i.e. 34,398.
Initially, let there be 100 goats. Then
100 == 40% ↑==> 140 == 30%↓(declined to 70%) ==> 98 == 30%↑ ==> 127.4 == 10%↓(sold) ==> 114.66
Hence, % increase = 14.66% [As 100 becomes 114.66]

Total employees = 1600
Female employees, 60% of 1600
$$ = \frac{{60 \times 1600}}{{100}} = 960$$
Then male employees = 640
50% of male are computer literate,
= 320 male computer literate
62% of total employees are computer literate,
$$ = \frac{{62 \times 1600}}{{100}} = 992$$     computer literate
Thus, Female computer literate = 992 - 320 = 672

Alternatively :
Let 60% employees are female and 40% are male
Then, 20% of male are computer literate and 42% are female computer literate
Female computer literate $$ = \frac{{1600 \times 42}}{{100}} = 672$$

Price after third depreciation,
100 ==25%↓ ==> 75 == 20%↓==>60 == 15% ↓ ==> 51
The price will be,
= Rs. 5,10,000

Alternatively :
1000000 × 0.75 × 0.80 × 0.85
= Rs. 5,10,000