Let there is 100 kg of ore. 25% ore contains 90% off Iron that means 25 kg contains; $$\frac{{25 \times 90}}{{100}} = 22.5\,{\text{kg}}\,{\text{iron}}$$ 22.5 kg Iron contains 100 kg of ore. Then, 1 kg of iron contains = $$\frac{{25}}{{100}}{\text{kg}}\,{\text{ore}}$$ Hence, 60 kg iron contains
= $$\frac{{100 \times 60}}{{22.5}}$$
= 266.66 kg ore

Let Ashu's salary = 100; Ashu's salary after rise = 125 Then Vicky's salary = 175 Vicky's salary after rise of 40% = 245 [As 10% of Vicky's salary is 17.5 then 40% = 17.5 × 4 = 70] Difference between Vicky's salary and Ashu's salary = 245 - 125 = 120 % more Vicky's salary than Ashu's = $$\frac{{120 \times 100}}{{125}} = 96\% $$

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

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 = $$\frac{{90}}{{12}}$$ = 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

Let 100 kg of hematite be obtained then 20% of it get wasted that means 80 kg of ore remains. Pure iron = 25% of remaining ore = $$\frac{{80 \times 25}}{{100}} = 20\,{\text{kg}}$$ 20 kg pure Iron is obtained from 100 of hematite 1 kg pure Iron is obtained from = $$\frac{{100}}{{20}}$$ hematite Then, 80000 kg pure Iron is obtained from =$$\,\frac{{100}}{{20}} \times 80000 = \,$$    $$400000\,{\text{kg}}$$   hematite.

Let the number of bacteria in the 1st generation be x, then number of bacteria in 2nd, 3rd, 4th . . . . . Generation would be $$8\left( {\frac{{\text{x}}}{2}} \right),\,8\left( {\frac{{4{\text{x}}}}{2}} \right),\,8\left( {\frac{{16{\text{x}}}}{2}} \right)$$     . . . . 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.

The total cost for the year
= 250000 + 2% of 2500000 + 2000
= Rs. 257000 For getting return of 15% he must earn
= $$\frac{{257000 \times 15}}{{100}}$$
= Rs. 38550 per year Then, Monthly Rent
= $$\frac{{38550}}{{12}}$$
= Rs. 3212.5

Passed in none = 5% Passed in all = 5% Passed in four = 20% of 90% = 18% Passed in one = 25% of 90% = 22.5% Passed in two = 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

Number of Indians men present there = $$\frac{{700 \times 20}}{{100}} = 140$$
Indian women = $$\frac{{500 \times 40}}{{100}} = 200$$ Indian children = $$\frac{{800 \times 10}}{{100}} = 80$$ Total member present in climate conference = 700 + 500 + 800 = 2000 Total Indian = 200 + 140 + 80 = 420 Hence, % of Indian present there = $$\frac{{420 \times 100}}{{2000}} = 21\% $$ % of people who were not Indian = 100 - 21 = 79%

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

Let the marks obtained in five subjects be 6x, 7x, 8x, 9x and 10x. Total marks obtained = 40x Max. Marks of the five subjects = $$\frac{{40{\text{x}}}}{{0.6}}$$   [40x is 60% of total marks] Max. Marks in each subject = $$\frac{{40{\text{x}}}}{{0.6 \times 5}}$$   = 13.33x Hence, % of each subject = $$\frac{{6{\text{x}} \times 100}}{{13.33}}$$   = 45.01% Or, $$\frac{{7{\text{x}} \times 100}}{{13.33}}$$   = 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

Let Ram's salary be x He spends on rent = 30% of x = $$\frac{{30{\text{x}}}}{{100}}$$ He spends on education = 30% from rest of the salary = $$\frac{{30 \times 70{\text{x}}}}{{100 \times 100}} = \frac{{21{\text{x}}}}{{100}}$$ He Spends on clothes = 24% of total salary = $$\frac{{24{\text{x}}}}{{100}}$$ Saving = 2500 Salary of ram = x $$\eqalign{ & \frac{{30{\text{x}}}}{{100}} + \frac{{21{\text{x}}}}{{100}} + \frac{{24{\text{x}}}}{{100}} + 2500 = {\text{x}} \cr & {\text{or,}}\,\frac{{75x}}{{100}} = {\text{x}} - 2500 \cr & {\text{or,}}\,75{\text{x}} = 100{\text{x}} - 250000 \cr & {\text{or, }}100{\text{x}} - 75{\text{x}} = 250000 \cr & {\text{or, x}} = \frac{{250000}}{{25}} \cr & {\text{or, x}} = 10000 \cr & {\text{Ram's}}\,{\text{salary = Rs}}{\text{.}}\,10000 \cr} $$

Let x be the page required when report is retyped
Now, we can use work equivalence method
20 × 55 × 65 = 70 × 65 × x
Or, x = $$\frac{{20 \times 55 \times 65}}{{70 \times 65}}$$
Or, x = 15.70 = 16 pages.
Hence, % reduction in pages = $$\left( {20 - 16} \right) \times \frac{{100}}{{20}}$$   $$\, = \,$$ $$20\% $$

Increase in the price of sugar = (8 + 2) = 10% Hence, price of sugar on, Jan. 1, 1996 $$\eqalign{ & = \frac{{20 \times 110 \times 110}}{{100 \times 100}} \cr & = {\text{Rs}}{\text{.}}\,24.20 \cr} $$

Let the number be x According to the question, 91 - $$\frac{{30{\text{x}}}}{{100}}$$ = x 9100 - 30x = 100x Or, 9100 = 130x Or, x = $$\frac{{9100}}{{130}}$$ Hence, x = 70

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%

Time lost over two weeks = 25% a week time(given that $$\frac{1}{2}$$ % clock loses in first week and in the second week it gains $$\frac{1}{4}$$ % on true time) A week = 168 hours Hence, clock lost = 0.42 hours = 25.2 minutes or 25 minute 12 seconds Thus, correct time = 11 : 34 : 48

100000 == 10%↑(1st year) ==> 110000 == 10%↑(2nd year) ==> 121000 Population at starting of 3rd year = 121000 [By using net percentage change method, we have saved our self from cumber some formulas on population which is based on compound interest].

$$\eqalign{ & {\text{Shrinking of cloth}}, \cr & = {\frac{{ {36 - 33} }}{{36}}} \times 100 \cr & = \frac{{100}}{{12}}\% \cr & {\text{Second time the strip shrinks,}} \cr & = \frac{{ {48 \times 100} }}{{1200}} \cr & = 4\,\text{inches} \cr & {\text{hence,}}\,{\text{the}}\,{\text{cloth}}\,{\text{remains}} \cr & = 48 - 4 \cr & = 44 \cr} $$

Let length, breadth and height of the room be 3, 2, 1 unit respectively. Area of walls = 2(l + b) × h = 2(3 + 2) × 1 = 10 sq. unit. Now, length, breadth and height of room will become 6, 1 and $$\frac{1}{2}$$ respectively. Now, area of walls = $$2\left( {6 + 1} \right) \times \frac{1}{2}$$   = 7 sq. unit. % decrease in the area of walls = $$\left( {10 - 7} \right) \times \frac{{100}}{{10}}$$   = 30%