Discussion Room : Quant

@zabeer zabeer sir ek profit loss ka doubt hai i cant calculate the initial and final amount plz help..
A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Rs. 240. What is the original price per kg of sugar?

@vinaycat2017
Let original price be x per kg
So initially, we could buy 240/x kg for 240 rupees
Now the new price is 0.8 x (20% reduction in x)
So now we can buy 240/0.8x kg for 240 rupees
The difference, 240/0.8x  240/x = 6 kg (given)
240/x (1.25  1) = 6
x = 240 * 0.25/6 = 40 * 0.25 = 10 rs / kg would be the original price.

Find number of whole number solutions of a + b + c + d = 20 where a, b, c and d ≤ 8
= 23c3  4 * 14c3 + 4c2 * 5c3
= 1771  1456 + 60
= 375why 60 is as added here, if we go by the common way for odthis instead of coefficient method:
(9+a')+(b+c+d) =20
a'+b+c+d=11so total ways= 23C3 4*14c3.=315
which 60 cases need to be added here?
Could anyone expalin the part?

Question : A does half as much work as B in 3/4th of the time. Together they take 18 days to complete the work. How much time shall B take to do it?
Did it as follows.
Assumed B takes 12 days to to do 12 work. (Rate 1w/day)
So, A does 6 work(half as much as B) in 9 days (3/4th of the time taken by B to do the same) so the rate is 6/9 = 2/3 work per day)
Given they take 18 days to complete the work. One day they do (1+2/3) = 5/3 work, in 18 days they do 30 work.
Hence B shall take 30 days to do 30 work since the rate of B is 1w/ day.But the answer given is 45 days.
Is there any logic fail in the method I used?

In how many ways 8 friends be arranged in a row if three of the friends do not want to sit at the
extremes?pls explain?

@aadirs 30 days is correct I guess.
1/a + 1/b = 1/18
we know, a = 3b/2 (half the work in 3/4th time means full work in 1.5 times the time taken by b)
2/3b + 1/b = 1/18
5/3b = 1/18
b = 18 * 5/3 = 30

@zabeer
SIr

Sir one more...

is it 14 ?

4 dice are rolled, what is the probability that sum of numbers on 4 dice is 18?


For a regular hexagon,
Diagonal = 2L and W = √3 L
So in our diagram,
BC = xz = 12
Bx = Cz = 6√3
Shaded area = Area of Rectangle (BxzC)  Area of Right Triangle Czy
= 12 * 6√3  1/2 * 6 * 6√3
= 72√3  18√3
= 54√3What is the OA ?

a + b + c + d = 18
Number of ways = (n  1) C (k  1) = 18C3 = 816 (If a, b, c and d can be any natural number)
But in our case a, b, c and d can only be natural numbers less than 6.
So cases like 12 + 2 + 2 + 2 = 18 should be removed.
Say a = A + 6 (To find cases where a is > 6)
A + 6 + b + c + d = 18
A + b + c + d = 12
Number of ways = 11C3 = 165
similarly for b, c and d.
So we have 816  4 * 165 = 156 favourable cases.What's the OA ? Not sure about the calculations.. logic should be as explained.
This concept and various question types are explained in detailed in the below link  Please have a look, you won't have any issues with similar questions :)

@zabeer test test test test