Let, a=1, b=2, c=3,d=4,e=5

S= 1/2+3/4+1/5

a এর সাথে আরো 1 যোগ করলে (1+1)/2 =1

greatest increase in S would result from adding 1 to the value of  A

In a right angled triangle, the radius of the incircle is given by the following relation .

As the given triangle is a right angled triangle, radius of its incircle

  = 2 units.

here, radius of in circle = 2(area of triangle)/sum of sides = 60/30=2 units

here, a+b/2=45 or,a+b=90 again, b+c/2=35 or,b+c=70 so, a+b-b-c=90-70=20

Suppose, number of people =10 total expenditure= G per person pay= g/10 if n number of people are added then per person pays=G/10+n so, expenditure reduces= G/10-G/10+n=Gn/100+10n  

People =10

Total cost=G dollar

Per person cost= G/10 dollar

If n additional people want to contribute to pay for the gift then Per person cost =G/(10+n)

Reduced = G/10- G/(10+n) = Gn/(100+10n)

here, here, value of n is lesser  than 50 and greater than 20. And if the number is divided by 5 remains 2. so,the number could be 22,27,32,37,42,47 again, after distributing among 6 children remains 1 so the number could be 25,31,36,43,49 here, 37 fills both the conditions. so,n=37 so,after distributing seven children remains=2

Area of a circle = Pi * (radius)2, where Pi = (22/7) When the length of the rope is increased to 30 m, grazing area becomes = (22/7) * 302 sq m. Therefore, the additional area it could graze when length is increased from 19m to 30m = 22/7*(302- 192) sq m. It can be simplified as (22/7)*(30+ 19)(30 - 19)=(22/7)*49*11 = 1694 sq m.

Imagine just one face of the 5x5 cube. (I'm imagining this massive Rubik's cube Which of the 1x1 cubes will have paint on only one face? Only those which are not on the edges - these will share a painted face with another side. The cubes that are not part of the edge form a 3x3 grouping of 1cm cubes. Therefore each face has 9 cubes that are painted one color. Since there are 6 faces we get 6x9 = 54.

The sum grew to 240 at the end of 2 years.

At the end of another 3 years, the sum grew to  300.

i.e. in 3 years, the sum grew by  60.

Therefore, each year, it grew by  20.

Sum at the end of 2 years =  240

Sum grew by  20 each year.

Hence, in the first 2 years, sum grew by 2 * 20 =  40.

Therefore, sum at the beginning of the period = Sum at the end of 2 years - 40 =  240 -  40 =  200.

Car averages x miles per gallon, means that 1 gallon is enough to drive x miles. We are asked to find average miles per gallon (miles/gallon) --> average miles per gallon would be total miles driven divided by total gallons used (miles/gallon). Total miles driven is 10+50=60. As car averages 25 miles per gallon in the city for 10 miles in the city it will use 10/25=0.4 gallons; As car averages 40 miles per gallon on the highway for 50 miles on the highway it will use 50/40=1.25 gallons; So average miles per gallon equals to

suppose,

distance from office to home=x difference of time=(8+4)=12 minute=1/5 hour here, x/7-x/8=1/5 or,8x-7x/56=1/5 so,x=11.2 so,distance =11.2 km

here, total pipe=8 suppose, pipe that fiils the tank =x so pipes that empty the tnk=8-x according to question, in 8 hours fills  1 tank in 1 hour   fills  1/8 tank so,x number of pipe  feels  x/8 part of tank in 1 hour again, (8-x) number of pipes empty   8-x/6 part of the tank in 1 hour here, x/8-(8-x)/ 6=1/5 or,x=4 so, pipe that fiils the tank =4

Profit- 19100

Badrul receive= 9600

Alim receive= 19100-9600 = 9500

Alims total investment= (10000 X 4)+(8000X5)+(5000 X 3)= 95000

9500 tk profit if investment 95000 tk

9600 tk profit if investment 96000 tk

Badruls investment = 96000/12=8000 tk

A's cost price = x tk

25% of x = 1000

x=800

A's profit = 1000-800 =200

B's profit = 25% of 1000 = 250 tk

B's profit greater than that of Merchant A = 250-200 =50 tk

 minimum number of marbles she must take out of her pocket to ensure that she has one of each color =(8+4+4+1) = 13