[pendyal]

Originally Posted by 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

area of the sector = (1/2) x r^2 X theta as you pointed out with theta being in radians.......in this case the value of theta is 1 hence the area becomes (1/2) x 8 x 8 and (1/2) x 2 x 2.

to arrive at the value of theta in radians, we divide the length of the arc by the radius or in other words, theta = l/r = 8/8 = 1

[pendyal]

Originally Posted by 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.....

let the number of 4s be p..... since the number is divisible by 72, it is divisible by 9...therefore sum of all 4s + sum of all 6s should be divisible by 9 or in other words

4 x p + 6 x (12-p) should be divisible by 9 this can happen only if p = 9

therefore the maximum number of 6s in the number can be 3

[naga25french]

Originally Posted by 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

for 150 units he gets 8000

for 200 unit he gets 9000...

taking difference --> 50 units gives him 1000 rupees incentive...

for 1 unit it will be 20rs

so for 400 units , 200 units + 200 units = 9000 + 20(200) = 13000

so salary per unit = 13000/400 = 32.5

[TheVacuum]

Originally Posted by 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.....

option (1), the number is 664444444464

[pendyal]

Originally Posted by 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

let his fixed salary be f and variable salary per unit be v

salary when he sells 150 units is f + 150v = 8000
salary when he sells 200 units is f + 200v = 9000

subtracting first equation from second equation we get 50v = 1000 or v = 20

substituting back in either equations gives f = 5000

now when he sells 400 units, total salary = f + 400v = 5000 + 400x20 = 13000

salary per unit will then be 13000/400 = 32.5 as you mentioned

[akhilmisra]

Originally Posted by 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

let x be fixed sal. and y be the incentive per unit
x + 150y=8000
x + 200y=9000

=> y=20 , x=5000

for 400 units total income =x + 400y
=5000 + 400*20
=13000
therefore income per unit =13000/400 = 32.5

[prateek7563]

Originally Posted by $U!\!$H|!\!E

Answer shoub be 21:
NB: Divisibility by 9:
Sum of the digits of the number must be divisible by 9.
Set 1:{1,1,1,6} - 2 ways eg: 1116, 6111
Set 2:{2,2,2,3} - 2 ways eg: 2223,3222
Set 3:{3,3,3,(0,9)} - 2+1 = 3 ways eg: 3339,9333,3330
Set 4:{4,4,4,6} - 2 ways eg: 4446,6444
Set 5:{5,5,5,3} - 2 ways eg: 5553,3555
Set 6:{6,6,6,(0,9)} - 2+1 = 3 ways eg: 6669,9666,6660
Set 7:{7,7,7,6} - 2 ways eg: 7776,6777
Set 8:{8,8,8,3} - 2 ways eg: 8883,3888
Set 9:{9,9,9,(0,9)} - 1+1 = 2 ways eg: 9999,9990
Set 10:{9,0,0,0} - 1 ways eg: 9000
So (2+2+3+2+2+3+2+2+2+1) = 21

my friend the question says that it has exactly 3 equal numbers consecutively, 9999 has four equal numbers!!!!!

[naga25french]

Originally Posted by 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.....

8 * 9 = 72 .. so number is definitely divisible by 9..

lets assume equal number of 6's and 4's .. so sum will be 60 ...

so automatically u should think to reduce 6 from it..

how ??

simple replace 3 6's by 3 4's ... actually it takes lot of time to explain but certainly take less than min to solve .. hope this helps..

[naga25french]

i like this particular question ... its actually IIFT 2008 question

A ladder 25 meters long is placed against a wall with its foot 7 meters away from the foot of the wall. How far should the foot be drawn out so that the top of the ladder may come down by half the distance of the total distance if the foot is drawn out?
A. 6 meters
B. 8 meters
C. 8.75 meters
D. None of the above



happy solving

[pendyal]

Originally Posted by naga25french

i like this particular question ... its actually IIFT 2008 question

A ladder 25 meters long is placed against a wall with its foot 7 meters away from the foot of the wall. How far should the foot be drawn out so that the top of the ladder may come down by half the distance of the total distance if the foot is drawn out?
A. 6 meters
B. 8 meters
C. 8.75 meters
D. None of the above



happy solving

let the ladder be drawn out by l

if i understood the question correctly, the height must be reduced by l/2

initially the ladder was 7m away from the wall. therefore it was placed at a height of 24m against the wall.

afterwards, the corresponding figures will be (7+l)m and (24-(l/2))m

using pythagorus theorem, (7+l)^2 + (24-(l/2))^2 = 25^2

solving we get l = 8m