# QUESTIONS ON PERCENTAGE (PART-IV)

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## 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’)