QUESTIONS ON PERCENTAGE (PART-IV)

QUERY 31

Consider two forms of diluted milk A and B with equal quantity in each. A has 80% milk while B has 60% percent milk. Now consider the following process and tell the final percentage of water in A. First, 10% of A is mixed with B and then 10% of B is mixed back with A.

A) 21.98%
B) 20%
C) 18.76%
D) 23%

MAHA GUPTA
Let the total liquid in A and B be 100 ml each.

So, milk in A = 80 ml, and water = 20 ml.

And milk in B = 60 ml, and water = 40 ml.

CASE-I
As 10% of A is mixed with B, so milk out of the mixture = 10% of 80 = 8 ml, and water out of it = 10% of 20 = 2 ml.

Thus milk left in A now = 80 – 8 = 72ml, and water left in A now = 20 – 2 = 18 ml, Total in A now = 72 + 18 = 90 ml

And milk in B now = 60 + 8 = 68 ml, and water in B now = 40 + 2 = 42 ml.

CASE-II
As 10% of B is mixed with A. so milk out of the mixture = 10% of 68 = 6.8 ml, and water out of it = 10% of 42 = 4.2 ml.

Total of milk and water out of B = 6.8 + 4.2 = 11 ml

Total of milk and water now in A = 90 + 11 = 101 ml

Water now in A = 18 + 4.2 = 22.2 ml

Therefore in percentage of water now in A = (22.2/101)* 100 = 21.98% (appox) [option ‘A’]

QUERY 32

During a certain season, a team won 80% of its first 100 games and 50% of its remaining games. If the team won 70% of its games for the entire season, what was the total number of games that the team won?

A) 170
B) 156
C) 150
D) 105

MAHA GUPTA
Let the remaining games i.e.the team won 50% of which = x
Therefore total games = 100 + x

Now according to the question
80% 100 + 50% of x = 70% of (100 + x)

=> 80 + x/2 = (100 + x)*7/10

Solving
x = 50

Each side of 80 + x/2 = (100 + x)*7/10 represents the total number of game won obviously, which we have to find. As both sides are equal put value of x in any to get the answer. Let’s take it LHS of this equation:

80 + 50/2 = 105 (option ‘D’)

QUERY 33

There are 100 students in a class out of which 99% are girls. How many girls should leave the class so that there percentage then is 98?

A) 1
B) 2
C) 3
D) 50

MAHA GUPTA
99% girls out of 100 means boys = 1 and girls = 99
Now let the number of girls leaving the class = x

Hence total students now = 100 – x
And total girls now = 99 – x

But girls now are 98% of total, means 98% of (100 – x)

Hence, (99 – x)/(100 – x) = 98/100
On solving, x = 50 (option ‘D’)

FASTER APPROACH
There were 99 girls and 1 boy

As, now some girls have left and there percentage is now 98, means 2 boys and 98 girls if the number in total is 100

But the number of boys is fixed i.e. 1

So we can say that if boys are 2 girls are 98
If boys is 1 the girls are 98/2 = 49

Therefore the number of girls leaving the class = 99 – 49 = 50 (option ‘D’)