[pendyal]

Originally Posted by priyalli

The consumption of diesel per hour of a bus varies directly as square of its speed .When the bus is travelling at 40 kmph its consumption is 1 litre per hour.if each litre cost rs 40 and other expences per hour is rs 40,then what would be the minimum expenditure required to cover a distance of 400 km ??


pls ealborate thru steps

Rs. 800 at a speed of 40....

let the consumption be c and total cost C....speed is v and hours is h

h=400/v

also c= k.v^2 and given that when v = 40, c = 1, k = 1/1600

now C = c.40.h + 40.h
= v^2.40.h/1600 + 40.h
= v^2.40.400/(1600.v) + 40.400/v
= 10.v + 16000/v

now differentiating C wrt v we will get the differential as 10 - 16000/v^2, equating this to zero we will get v = 40
if we differentiate C twice wrt to v we will see that the result is 32000/v^3 which is positive at v = 40 making v = 40 a minima.....

the cost works out to Rs. 800 substituting v = 40 in the formula for C.....

if i am not to use differentiation then
C = 10v +16000/v
= 400 (v/40 + 40/v)

now we know that x + 1/x is least when x = 1 subsitituting v/40 for x, we get v/40 = 1 or v = 40

[raajamurugan]

s de ans 10 m/s... if tat s it then the soln s simple..

[raajamurugan]

Originally Posted by shilpakokkanti

In a 100 m race,A beats B by 20 m and B beats c by 7.5 sec.Wht is B'sspeed if A runs twice as fast as C.??
This is an easy question.. but i am very poor in time and distance..please help me out..

s da ans 10 m/s

[pendyal]

Originally Posted by shilpakokkanti

In a 100 m race,A beats B by 20 m and B beats c by 7.5 sec.Wht is B'sspeed if A runs twice as fast as C.??
This is an easy question.. but i am very poor in time and distance..please help me out..

A beats B by 20 m meaning in the time A had run 100 metres, B ran 80 metres.....since the times are constant, the ratio of the speeds of A and B are the same as the distances covered or 100:80 or 5:4. Now A:C = 2:1 meaning when A covered 100 metres, C covered 50. combining the two ratios, i will get ratio of speed of B to C as 8:5

let the speeds be 8x and 5x
time taken by B is 100/8x and time taken by C is 100/5x
second statement is saying that B beat C by 7.5 seconds, so difference of their times is 7.5 seconds.....

(100/5x) - (100/8x) = 7.5

taking x to the other side (100/5) - (100/ = 7.5x
20 - 12.5 = 7.5x
7.5 = 7.5x
or x = 1

meaning speed of B is 8x or 8 metres per second.....

[arya5139]

Originally Posted by shilpakokkanti

In a 100 m race,A beats B by 20 m and B beats c by 7.5 sec.Wht is B'sspeed if A runs twice as fast as C.??
This is an easy question.. but i am very poor in time and distance..please help me out..

A beats B by 20 m => when A is at 100 , B is at 80

=>when A is at 125 ,B is at 100

since speed of A is twice that of C

when A is at 125,C is at 125/2 and B is at100

since B beats C by 7.5 sec => C takes 7.5 sec to cover (100 -125/2) = 75/2 m distance

=>speed of C = 75/2/7.5 = 5 m/s

=> speed of A = 10 m/s

=> speed of B = 80/100*10 = 8 m/s

[protoplasm]

Source: TestFunda

In the given diagram, AB and DC are arcs of concentric circles with centre O. The perimeter of the figure ABCD is 22 cm. What is the area of the figure ABCD?


Question :
i have a doubt in the RED step in the given solution

Perimeter of ABCD = length of arc AB + 6 + length of arc DC + 6 = 22 cm

∴ Length of arc AB + length of arc DC = 22 – 12 = 10 cm …(i)

∵ Sector OAB and sector ODC are similar,




∴ From equation (i),

Length of arc AB = 2 cm and length of arc DC = 8 cm

Now, area of figure ABCD = area of sector ODC – area of sector OAB


= 32 – 2

= 30 cm2


// whats the correct formula for area of a sector ?? in books , it says arc s = r x theta and area = (1/2) x r x s = (1/2) x r x r x theta = (1/2) x r^2 x theta .....but in the above they used the triangle's area calculation formula (1/2) x base x height...arc and height is not same....is this fare ? .......how come we ignore the role of theta here and forget the generic formula ??.

Thanks

[amchithecoolest]

1>if 1+sec thita +tan thita =p,then cos thita is
(1)(p-1)/(p^2-2p+2) (2)2(p-1)/(p^2-2p+2)
(3)(p-1)/(p^2+2p+2) (4)2(p-1)/(p^2-2p+1)
(5)(p-1)/(p^2+2p+1)

[one down]

a 12 digit no divisible by 72 consists of only 4's and 6's
find the no of 6's in the largest poss such no....
1) 3
2) 4
3) 5
4) 6


help plzz.....

[TheVacuum]

Originally Posted by amchithecoolest

1>if 1+sec thita +tan thita =p,then cos thita is
(1)(p-1)/(p^2-2p+2) (2)2(p-1)/(p^2-2p+2)
(3)(p-1)/(p^2+2p+2) (4)2(p-1)/(p^2-2p+1)
(5)(p-1)/(p^2+2p+1)

option (2) by sub theta = 45 deg

[priyalli]

A salesman for a company gets an incentive for every unit of product he sells apart from his fixed salary .he gets rs 8000 and rs 9000 for 150units and 200 units he sold respectively .If he sells 400 units ,what is his income per unit?

ans:rs 32.5
pls elaborate thru steps