Practice Test: Percentages - 1 - UPSC

Let the number of apples be 100.

On the first day, he sells 60% apples ie.,60 apples. Remaining apples =40.

He throws 15% of the remaining i.e., 15% of 40 = 6.Now he has 40 - 6 = 34 apples

The next day he throws 50% of the remaining 34 apples i.e., 17.

Therefore, in all, he throws 6 + 17 =23 apples.

The correct answer is A. 

 Total votes = 12000.
 Total Valid votes = 85% of 12000 = 10200.
 Walter gets 80% of 10200 votes = 8160 votes.
 Jesse Pinkman would get 10200 – 8160 = 2040 Votes. 

Given:
a% of b = (a/100) x b = ab/100
30% of a% of b = 30% of ab/100
= (30/100) x ab/100
= 3ab/1000

Also Given:
b% of c = (b/100) x c = bc/100
25% of b% of c = 25% of bc/100
= (25/100) x bc/100
= bc/400

Now ATQ:
(3ab/1000) = (bc/400)

⇒ 3a/10 = c/4
⇒ c = 12a/10
⇒ c = 1.20a

Let the number be 100. Then, 200 should be the correct outcome. But instead, the value got is 50.
 Change in value = 200 – 50 = 150.
 The percentage change in the value = 150 X 100 / 200 = 75%.
 Alternatively, you could think of this as the number being ‘x’ and the required result being 2x and the derived result being 0.5x.

 Hence, the percentage change in the result is 1.5x X 100 / 2x. Clearly, the value would be 75%. (Note: In this case, the percentage change in the answer does not depend on the value of ‘x’). 

Alternate solution :

Let the number be x.

Then actual value should be 2x and the measured value is x/2.

Therefore, the percentage error can be calculated as:

Actual value−Measured value/Actual value×100

=2x−x/2/2x×100

=4x−x/2/2x×100

=3x/2×1/2x×100

=3/4×100

=75%

Let the population of Mexico be X Pop. 

After 10% migrated to SA = 1-0.1= 0.9x

Population after 10% migrated to America = 0.9x * 0.9 = 0.81x Population after 10% of the rest migrated to Australia = 0.81x * 0.9 = 0.729x

Let the no of males be a and females be b => a+b = 0.729x Given that b=a/2 ratio didn't change after and before migration so,

b = 364500

=> a = 2*364500 = 729000

=> 729000 + 364500 = 0.729x

=> x = 1500000

 From the first statement we get that out of 100 litres of the mixture, 25 litres must be milk.
 Since we are adding water to this and keeping the milk constant, it is quite evident that 25 litres of milk should correspond to 20% of the total mixture.
 Thus, the amount in the total mixture must be 125, which means we need to add 25 litres of water to make 100 litres of the mixture. 

Let the initial side of the cube be 'x' units.

⇒ Surface area of cube =6×side²=6x² square units

Given, the length, breadth and height of a cube are decreased, decreased and increased by 5%, 5% and 20% respectively.

This means that the cube is now converted into a cuboid.

Length of cuboid =(100-5)% of x=95% of x=19x/20

Breadth of cuboid =(100-5)% of x=95% of x=19x/20

Height of cuboid =(100+20)% of x=120% of x=24x/20

⇒ Surface area of cuboid =2[(19x/20×19x/20)+(19x/20×24x/20)+(24x/20×19x/20)]

=2[(361x²/400)+(456x²/400)+(456x²/400)]

=2×[1273x²/400]=1273x²/200 square units

⇒ Increase in surface area ={[(1273x²/200)-6x²]  / [6x²]}×100=(73/1200)×100=6.0833%

Hence, the correct answer is 6.0833%.

 Let the initial price of raw materials be 100.
 The new cost of the same raw material would be 115.
 The initial cost of labour would be 25 and the new cost would be 30% of 115 = 34.5

 The total cost initially would be 125.
 The total cost for the same usage of raw material would now be: 115 + 34.5 = 149.5

 This cost has to be reduced to 125. The percentage reduction will be given by 24.5 / 149.5 = 16 % approx. 

Weight of first container = 100kg

According to the question,

Weight of the 3^rd container = 100 × 5/4 = 125 kg

Weight of the 2^nd container = 125 × 6/5 = 150 kg

Weight of the 4^th container = 175 kg

Weight of the 5^th container = 175 × 10/7 = 250 kg

Average of three heaviest container = (250 + 175 + 150)/3 = 191.66 kg

Average of three lightest container = (100 + 125 + 150)/3 = 125 kg

∴ Required answer = 191.66 – 125 = 66.66 kg