## Percentage Questions and Answers Part-5

1. A litre of water evaporates from 6L of sea water containing 4% salt. Find the percentage of salt in the remaining solution.
a) $$5\frac{1}{2}\%$$
b) $$3\frac{1}{2}\%$$
c) 3%
d) $$4\frac{4}{5}\%$$

Explanation:
\eqalign{ & {\text{Quantity of salt in 6L of sea water,}} \cr & = \frac{{ {6 \times 4} }}{{100}} = 0.24 \cr & {\text{Percentage of salt in 5L of sea water,}} \cr & = \frac{{ {0.24 \times 100} }}{5} = 4\frac{4}{5}\% \cr}

2. Two discount of 8% and 12% are equal to a single discount of:
a) 20%
b) 19.04%
c) 22.96%
d) 22%

Explanation: After first discount,
100 ---- 8%↓ ----> 92
After second discount,
92 ---- 12%↓ ----> 80.96
Single discount = 100 - 80.96 = 19.04%

3. In a library 60% of the books are in Hindi, 60% of the remaining books are in English rest of the books are in Urdu. If there are 3600 books in English, then total no. of books in Urdu are:
a) 2400
b) 2500
c) 3000
d) 3200

Explanation: Let there are X books in the library.
Number of Hindi books = 60% of X = $$\frac{{60{\text{X}}}}{{100}}$$  = 0.6X
Remaining Books = X - 0.6X = 0.4X
Number English books = 40% of reaming books = 60% of 0.4X = 0.24X.
Urdu Books = X-0.6X -0.24X = 0.16X
0.24X = 3600
X $$= \frac{{3600}}{{0.24}} = 15000$$
Urdu Books = 0.16X = 0.16 × 15000 = 2400

4. In Sabarmati Express, there as many wagons as there are the no. of seats in each wagon and not more than one passenger can have the same berth (seat). If the middlemost compartment carrying 25 passengers is filled with 71.428% of its capacity, then find the maximum no. of passengers in the train that can be accommodated if it has minimum 20% seats always vacant.
a) 500 seats
b) 786 seats
c) 980 seats
d) 1060 seats

Explanation: Total number of passenger in each compartment = $$\frac{{ {25 \times 7} }}{5}$$  = $$35$$
Total berth = 352 = 1225
Maximum available capacity
\eqalign{ & = \frac{{ {1225 \times 80} }}{{100}} \cr & = 980\,{\text{seats}} \cr}

5. The population of a village is 5000 and it increases at the rate of 2% every year. After 2 years, the population will be:
a) 5116
b) 5202
c) 5200
d) 5204

Explanation:
\eqalign{ & {\text{Population after two years}}, \cr & = 5000 \times {\left[ {1 + {\frac{2}{{100}}} } \right]^2} \cr & = 5202 \cr}

6. The schedule working hour of a labour in a week if 48 hours and he gets Rs. 480 for that. Over time rate is 25% more than the the basic salary rate. In a week a labour gets Rs. 605, how many hours altogether he works in that week.
a) 49 hours
b) 52 hours
c) 55 hours
d) 58 hours

Explanation: Schedule working hours in week = 48
Total pay in a week for schedule working hours = Rs. 480
Pay per hour for schedule working hours = $$\frac{{480}}{{48}}$$ = Rs. 10
Pay per hour for over time = 10 + 25% of 10 = Rs. 12.5
Total pay in that particular week = Rs. 605
Extra pay = 605 - 480 = 125
So, total over time = $$\frac{{125}}{{12.5}}$$  = 10 hours
Total work hour altogether in that week = 48 + 10 = 58 hours

7. In an election 4% of the votes caste become invalid. Winner gets 55% of casted votes and wins the election by a margin of 4800 votes. Find the total number of votes casted.
a) 45000
b) 48000
c) 50000
d) 52000

Explanation: Winner gets 55% of votes.
As 4% votes were declared invalid so 96% would be the valid votes
So, Winner gets 55% of 96% valid votes
Winner gets % valid votes = $$\frac{{55 \times 96}}{{100}}$$   = 52.8% votes
Loser gets = 96 - 52.8 = 43.2% votes
Difference = 9.6%
9.6% = 4800
1% = $$\frac{{4800}}{{9.66}}$$
100% Votes = $$\frac{{4200 \times 100}}{{9.66}}$$   = 50000
Total Voters = 50000

8. A reduction of 10% in the price of cloth enables a man to buy 6 meters of cloth more for Rs. 2160. Find the reduced price and also the original price of cloth per meter.
a) Rs. 36, Rs. 40
b) Rs. 40, Rs. 36
c) Rs. 36, Rs. 44
d) Rs. 44, Rs. 36

Explanation: Money spent originally = Rs. 2160
Less money to be spent for now for the same length of cloth,
= 10% of 2160 = Rs. 216
It means Rs. 216 enables a man to buy 6 meters of cloth
Reduced price = $$\frac{{216}}{6}$$ = Rs. 36 per meter
Original price = $$\frac{{100 \times 36}}{{90}}$$   = Rs. 40 per meter

9. A gardener increased the rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden:
a) Has increased by 20%
b) Has increased by 12%
c) Has increased by 8%
d) Is exactly the same as the old area

Explanation: Let original area of the garden was 100 square unit.
Increase or decrease in area can be easily determined by this graphic:
100 == 40% up length ==> 140 == 20% down width ==> 112 (Final Area)
There is 12% increase in area of the garden.

10. If A exceeds B by 40%, B is less than C by 20%, then A : C is
a) 28 : 25
b) 26 : 25
c) 3 : 2
d) 3 : 1

X = $$\frac{{100}}{{0.8}}$$ = 125
A : C = $$\frac{{140}}{{125}}$$ = 28 : 25