Test Level 3: Percentages - CAT MCQ

Option (4) is correct.
Let quantity A be x.
Two successive increase of 20% on x gives us 1.44x.
Let quantity B be y.
Three successive increase of 10% on y gives 1.331y.
Now, 80% of 1.331y = 1.44x
x = 0.739y
That is, x is 74% of y.

Initially, vote share of X = 60%
Vote share of Y = 40%
According to the question, 15% of the vote share of X is added in vote share of Y; and 25% of the vote share of Y is added to the vote share of X.
Last day, total vote share:
Vote share of X = 60% - 9% + 10% = 61%
Vote share of Y = 40% - 10% + 9% = 39%
i.e X won by 22% by Y.
22% is equal to 22. (Given)
So, total number of votes is 100.
Vote share of X is 61%, i.e. 61 votes for X.

Let the price of 1 litre of ice cream be Rs. x and let Vaibhav initially buy 'y' litres of ice cream. Therefore, he would have spent Rs. xy on ice cream.
When the price of ice cream increases by 25%, the new price per litre of ice cream is 1.25x.
Vaibhav intends to increase the amount he spends on ice cream by 15%.
That is, he is willing to spend xy + 15% of xy = 1.15xy.
Let the new quantity of ice cream that he can get be 'q'.
Then, 1.25x × q = 1.15xy

As the new quantity that he can buy is 0.92y,
He gets 0.08y lesser than what he used to get earlier.
Or, a reduction of 8%.

Let x be the total number of people that will be asked for money.
Number of people already associated with the company = 0.6x
Number of remaining people = 0.4x
Total amount already collected = 0.6x × 600 = 360x
This amount represents 75% of total needed.
Company needs to raise 25% of total needed.
75% of total = 360x

So, the company needs to collect 120x from remaining 0.4x people to be solicited.
Average per person = 120x/0.4x = 300
So, average money collected from remaining people should be Rs. 300.

Total number of mobile phones and credit card holders = x% of p
Let the number of males be m.
So, the number of females = p - m
Thus, the number of mobile phones and credit cards held by males = y% of m
The number of mobile phones and credit cards held by females = z% of (p - m)
Thus, x% of p = y% of m + z% of (p - m)
Hence, m = p(x - z)/(y - z)
Thus, option (3) is the answer.

Let in the 1st round, 'a' members voted for the 2nd candidate.
Thus, in the 1st round, members who voted for the 1st candidate = 550 - a
In the 2nd round, number of member who voted for the 2nd candidate = 2.5a
So, number of members who voted for the 1st candidate = 550 - 2.5a
Now, combined votes of both the rounds for the 1st candidate = 550 - a + 550 - 2.5a = 1100 - 3.5a
Combined votes of both the rounds for the 2nd candidate = a + 2.5a = 3.5a
Now, according to the question, 1100 - 3.5a - 3.5a = 400
Or, a = 100
Thus, 100 members opposed the 1st candidate in the 1st round.
Hence, answer option 4 is correct.

Let the number of cold drinks sold be '3x',
Then, number of water bottles sold = 1/3 of 3x = x
Let the price of each bottle of cold drink be 'c' and that of each water bottle be 'w'.
Total collection from the sales of cold drinks and water bottles = (3cx + wx)
60% of the collection is from sale of cold drinks (given).

This implies, 10cx = 6cx + 2wx
Therefore, 4cx = 2wx
This implies, w = 2c
Had 30 more cold drinks been sold, its contribution would have been 80%.

This gives, 15cx + 150c = 12cx + 120c + 4wx
This implies, 15cx + 150c = 12cx + 120c + 4(2c)x
Hence, 5cx = 30c
This implies, x = 6
∴ Number of cold drinks sold = 3x = 3(6) = 18

Assume that the box contains x number of chocolates.

Remaining = 0.36x
Given:
0.36x - 8 = 0.35x
 x = 800
She had 800 chocolates.
She ate 0.2x + 0.12x = 0.32x = 256 chocolates.

Let the total milk be 100ℓ.
After first operation, amount of pure milk = 100 - 20 = 80ℓ
After second operation, total solution = 100ℓ
(80ℓ milk + 20ℓ water)
Amount of milk taken out 

Amount of pure milk left = 80 - 16 = 64ℓ
After third operation, total solution = 100ℓ(∵ of 64ℓ + 36ℓ)
Amount of milk taken out 

Amount of remaining pure milk = 64 - 12.8 = 51.2ℓ

He uses 24% fuel in covering 20% of the journey.
For next 25% of journey, he will consume 30% fuel.
So, for 45% of the journey in city driving conditions, 54% of the fuel is consumed.
Fuel efficiency = 45/54 = 5/6
Hence, for the remaining 55% journey, 46% fuel is left.
After increment, fuel efficiency = 55/46