Official Quant thread for CAT 2013

MBA CAT 2024
27188
@maroof10 said:
A person can dig a trench 40 m in depth in 4 days working 8 hrs a day.However,after every day he finds 1/5th of the depth got filled up with mud again. In how many days can he dig a trench 30m in depth?
in one day he will dig 10 m
which will become 4/5 *10 =8m next day
8+8+8=24
in 8 hours he digs 10 m
6 meter he will dig in 48/10=4.8 hours

3 days and 4 hours and 48 minutes?
27189

5 days ??

@maroof10
27190
@maroof10 said:
A person can dig a trench 40 m in depth in 4 days working 8 hrs a day.However,after every day he finds 1/5th of the depth got filled up with mud again. In how many days can he dig a trench 30m in depth?
3days 4hours 48 minutes.
27191
@Subhashdec2 (1/5)th of the total is filled with mud and not of that particular day.
so,if 1st day he digs 10, effective is 8..
2nd day he again digs 10,effective is 18-(18/5) and so on.
27192

Q 31

27193
@maroof10

Shld be 3 days 4 hrs n 48 minutes..

Let x m/hr/day be the rate of wrk of the man..

Hence, x*4*8 = 40 , or, x=5/4 m/hr/day..(i)..Thus, In 1 day he will dug 10m worth of mud..

Now, 1st day = 10-2 = 8m[Since 1/5th of the mud dug is again filled]..2nd day = 8 m..3rd day= 8m..Thus, at the begging of 4th day, 24 m of mud has already been dug..

Now, in 4 hr of the 04th day he wud had dug 5 m..Thus, a total of 1 m is left..

Now, as per (i), it wud take 4/5th of an hr..

Hence, the total tym taken to dig the trench of 30 m is 3 days 4 hrs n 48 mins..
27194
@vbhvgupta Q31- C
1000
27195
@maroof10 said:
A person can dig a trench 40 m in depth in 4 days working 8 hrs a day.However,after every day he finds 1/5th of the depth got filled up with mud again. In how many days can he dig a trench 30m in depth?

confused in the refilling of mud..is it 1/5th of depth dug on that day or 1/5th of total depth till that point of time ?
27196
@vbhvgupta let initial price be y
therefore (x^2*y)/100 = 160
(x^2*(y-160))/100 =134.4

solving two we get y =1000
27197
@maroof10 said:
A person can dig a trench 40 m in depth in 4 days working 8 hrs a day.However,after every day he finds 1/5th of the depth got filled up with mud again. In how many days can he dig a trench 30m in depth?
assuming 1/5th of depth(on each day) OA = 3 days 4hrs 48 mins

assuming 1/5th of outstanding depth on each day..

getting a series

5/4 *8(4/5 + (4/5)^2 + (4/5)^3+....n terms) = 30

n = log 0.25/log 0.8 ( n in number of days) ??? confused
27198
@vbhvgupta

Shld be 1000..

Let y be the Original value..

Thus, y' = y(1 -{x/100}^2)..Given, y - y' = 160..

=>y - y(1 - {x/100}^2) = 160 , or, y*{x/100}^2 = 160...(i)

Again, y'' = y(1 - {x/100}^2)^2..Given, y' - y'' = 134.4

=>y(1 - {x/100}^2) - y(1 - {x/100}^2)^2 = 134.4

=>y(1 - {x/100}^2)*[1 -(1 - {x/100}^2)] = 134.4

=>y(1 - k^2)[k^2] = 134.4....where k =(x/100)

=>(1 - k^2)*160 = 134.4 ...From (i)

=> k^2 = 256/1600..Hence x = 40 n y = 1000...
27199

33

27200

40

27201

@maroof10 said:
A person can dig a trench 40 m in depth in 4 days working 8 hrs a day.However,after every day he finds 1/5th of the depth got filled up with mud again. In how many days can he dig a trench 30m in depth?
@chhabrakaran29 said:
@Subhashdec2 (1/5)th of the total is filled with mud and not of that particular day.so,if 1st day he digs 10, effective is 8..2nd day he again digs 10,effective is 18-(18/5) and so on.
considering the above,
i'm getting 6days and 0.38hours.

1st day 8, 2nd 14.4, 3rs 19.52, 4th 23.61, 5th 26.89, 6th 29.51..

correct me if i am wrong.
#paintful calc, i'm sure i've dropped the ball ..
27202
@Subhashdec2 the answer given is on the 5th day work is completed..I m also confused.
27203
@ChirpiBird the answer given is on the 5th day work is completed
27204
@vbhvgupta

Shld be 9600..

Let P be the total Profit n S be the salary..

Given, S = 1/5(P - S)..or, S = 1/6*P

Now, Total Capital = (20k + 30k)*12 = 600k

Thus, Profit earned by Goyal = 12*20k/(600k)*5/6*P + 1/6*P

=>2/6*P + 1/6*P => 1/2*P

Thus, 1/2*P = 4800..Hence, P = 9600..
27205
@pyashraj the answer given is on the 5th day work is completed
27206
@vbhvgupta 40 -D
2500
27207
@vbhvgupta said:
40
2500??