Percentage - 05

Explanation:-

Let the fraction be x/y.
When fraction is squared its numerator is reduced by 33(1/3) and denominator is reduced by 20%.

$$\eqalign{ & {\text{According}}\,{\text{to}}\,{\text{question}} \cr & {\left( {\frac{x}{y}} \right)^2} \times \frac{{33\left( {\frac{1}{3}} \right)\% }}{{20\% }} = 2\left( {\frac{x}{y}} \right) \cr & {\text{Or}},\,{\left( {\frac{x}{y}} \right)^2} \times \frac{{\left( {\frac{2}{3}} \right)}}{{\left( {\frac{1}{5}} \right)}} = 2\left( {\frac{x}{y}} \right) \cr & {\text{Or}},\,\frac{x}{y} = \frac{3}{5} \cr & {\text{Sum of numerator and denominator is}} \cr & \left( {x + y} \right) = 3 + 5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 8 \cr}$$

Explanation:-

$$\eqalign{ & {\text{According}}\,{\text{to}}\,{\text{question}} \cr & \left( {\frac{{XY}}{{100}}} \right) + \left( {\frac{{YX}}{{100}}} \right) \cr & = \frac{{2XY}}{{100}} \cr & = 2\% \,of\,XY \cr}$$

Explanation:-

Time lost over two weeks = 25% a week time(given that 1/2% clock loses in first week and in the second week it gains 1/4% on true time)
A week = 168 hours
Hence, clock lost = 0.42 hours = 25.2 minutes or 25 minute 12 seconds.
Thus, correct time = 12:25:12.

Explanation:-

Passed in none = 5%
Passed in all = 5%
Passed in four = 20% 0f 90% = 18%
Passed in three = 24.5%
Passed in three =(100-5-5-22.5-24.5-18) = 25%.
But given 300 students passed in three.
Hence, 25% = 300.
So, 100% = 1200.
1200 students must have appeared.

Explanation:-

Increase in the price of sugar = (8+2) = 10%
Hence, price of sugar on, Jan. 1, 1996
= (20*110*110)/(100*100) = Rs. 24.20.

Explanation:-

Let the number of bacteria in the 1^st generation be x, then number of bacteria in 2^nd, 3^rd, 4^th . . . . . Generation would be
8(x/2), 8(4x/2), 8(16x/2) . . . . And so on.
As x, 4x, 16x, 64x . . . . . it is in GP with common ratio 4.
Hence, 7th term of GP,
x(4)⁶ = 4096
Or, x = 1 or 1 million.

Explanation:-

Let the marks obtained in five subjects be 6x, 7x, 8x, 9x and 10x.
Total marks obtained= 40x
Max. Marks of the five subjects = 40x/0.6 [40x is 60% of total marks]
Max. Marks in each subject = 40x/0.6*5 = 13.33x
Hence, % of each subject = 6x*100/13.33 = 45.01%
Or, 7x*100/13.33 = 52.51
In same way other percentage are 60.01%, 67.52%, 75.01%.
Hence, number of subjects in which he gets more than 50% marks = 4.

Explanation:-

We solve it through options. Choosing options for trial depends on mental thought.
100 ==12% up ==>112 ==12% up ==>125.44 ==12% Up ==> 140.49
So, answer is 12%.

Explanation:-

Let us assume there are 100 students in the institute.
Then, number of boys = 60
And, number of girls = 40
Further, 15% of boys get fee waiver = 9 boys
7.5 % of girls get fee waiver = 3 girls
Total = 12 students who gets fee waiver
But, here given 90 students are getting fee waiver. So we compare
12 = 90
So, 1 = 90/12 = 7.5
Now number of students who are not getting fee waiver = 51 boys and 37 girls.
50% concession = 25.5 boys and 18.5 girls (i.e. total 44).
Hence, required students = 44*7.5 = 330.

Explanation:-

Let initial price of Maruti Car be Rs. 100.
As price increases 30%, price of car will become, (100 +30% of 100) = Rs. 130.
Due to increase in price, sales is down by 20%. It means, it is going make 20% less revenue as expected after increment of price.
So, New revenue = (130 - 20% of 130) = Rs. 104.
The initial revenue was Rs. 100 which becomes Rs. 104 at the end. It means there is 4% increment in the total revenue.

Mind Calculation Method:

100==30%↑(price effect)==>130==20%↓(sales effects)==>104.
Hence, 4% rises.