Hi All,
Can anybdy help me out in solving following doubt
What is the sum of the following infinite series:
1/1 + 1/3 + 1/6 + 1/10 + 1/15 ...
Thanx in advance.....
Bye
Sunil
if we observe the denominators ..we will find that each denominator=sum of all numbers from 1 to that particular n..i.e. 1+2+3+...n
eg. 2nd term=3=1+2;
3rd term=6=1+2+3;
4th term=10=1+2+3+4
i.e. nth term =n*(n+1)/2
thus we get the fraction as 2/{n*(n+1)} = 2 [ 1/n - 1/n+1]
thus the total sum = 2[1-1/(n+1)]
if n is infinite total sum=2
is this the answer?
Hi All,
Can anybdy help me out in solving following doubt
What is the sum of the following infinite series:
1/1 + 1/3 + 1/6 + 1/10 + 1/15 ...
Thanx in advance.....
Bye
Sunil
A thief steals four gallons of liquid soap kept in a train compartment's bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it is found that the ratio of liquid soap now left in the container to that of the wated in it is 36: 13. What was the initial amount of the liquid soap in the container if iti is konwn that the liquid soap is neither used nor augmented by anybody else during the entire period?
if we observe the denominators ..we will find that each denominator=sum of all numbers from 1 to that particular n..i.e. 1+2+3+...n
eg. 2nd term=3=1+2;
3rd term=6=1+2+3;
4th term=10=1+2+3+4
i.e. nth term =n*(n+1)/2
thus we get the fraction as 2/{n*(n+1)} = 2 [ 1/n - 1/n+1]
thus the total sum = 2[1-1/(n+1)]
if n is infinite total sum=2
is this the answer?
Hi Asima,
thanks for the reply.
I have a doubt in the explanation given by you , How the step marked in Red comes from the earlier step? I mean to say How 1/n has been converted to 1 marked in Blue.
if we observe the denominators ..we will find that each denominator=sum of all numbers from 1 to that particular n..i.e. 1+2+3+...n
eg. 2nd term=3=1+2;
3rd term=6=1+2+3;
4th term=10=1+2+3+4
i.e. nth term =n*(n+1)/2
thus we get the fraction as 2/{n*(n+1)} = 2
thus the total sum = 2
if n is infinite total sum=2
is this the answer?
Hi Asima,
thanks for the explanation. I have a doubt, in the explation how the step marked in Red has come from the last step? I mean to say how 1/n has been converted into 1(marketd in Blue) ?
parag_ca SaysA thief steals four gallons of liquid soap kept in a train compartment's bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it is found that the ratio of liquid soap now left in the container to that of the wated in it is 36: 13. What was the initial amount of the liquid soap in the container if iti is konwn that the liquid soap is neither used nor augmented by anybody else during the entire period?
Soln.
let the initial amt=x
after ist stealing &water; addn
qty of soap=x-4
water=4
after 2nd stealing & water addition
qty of soap=(x-4)-4*(x-4)/x
water=4-4*4/x+4= 8-16/x
Now,
((x-4)-4(x-4)/x )/(8-16/x) =36/13
after solving we get x=28
Chapter 4 LOD II Ques 12
Rajesh scored 65% in english and 82% in History. What is the minimum percent he should score in Sociology, which is out of 50 marks (if English and History were for 100 marks each), if he aims at getting 78% overall?
(a)94% (b)92% (c)98% (d)96%
u understood till the part that each term =2/(n*(n+1))
i.e. each term = 2{1/n- 1/(n+1)}
now when we sum up all the terms;
1st term =2{1/1-1/2}=2{1-1/2}
2nd term= 2{1/2-1/3}
3rd term=2{1/3-1/4}....
....
n-1th term= 2{1/(n-1)- 1/n)}
nth term = 2{1/n- 1/(n+1)}
on addind up all the terms you will notice that everything cancels out except 1 and 1/n+1;
and we get the sum as = 2{1 - 1/n+1}
Hi Asima,
thanks for the explanation. I have a doubt, in the explation how the step marked in Red has come from the last step? I mean to say how 1/n has been converted into 1(marketd in Blue) ?
marks in english= 65 (out of a total of 100 marks );
marks in history=82 (out of a total of 100 marks );
let marks in sociology be =x (out of a total of 50 marks );
then overall percentage = {(65+82+x)/(100+100+50)} *100
= {(147+x)/250} * 100 which is equal to 78
thus x=48
percentage in sociology= (48/50)*100 = 96 % (d)
Chapter 4 LOD II Ques 12
Rajesh scored 65% in english and 82% in History. What is the minimum percent he should score in Sociology, which is out of 50 marks (if English and History were for 100 marks each), if he aims at getting 78% overall?
(a)94% (b)92% (c)98% (d)96%
Hi all....I have managed to get an old copy of Arun sharma......is that enough or I should manage a latest version (if there is a latest version in the market).
Hope to hear from you all.
Thanks & Regards
Sarsij
how many times does the digit 6 appear when you count from 1000 to 9999 ?
a. 2700 b. 3700 c. 1500 d. None
how many times does the digit 6 appear when you count from 1000 to 9999 ?
a. 2700 b. 3700 c. 1500 d. None
The answer is
Between 1000 and 1999 6 comes 300 times( 20 times in each hundred numbers + 100 times in 1600-1699 for the hundred's place)
So between 1000 and 9999 it comes 300*10 = 3000
Additionally it comes 1000 times in 6000 - 6999 in the thousand's place So that makes the total 4000....Hence I think the ans is d
Regds,
Jigar
the answer given is (b)3700
n i had a doubt..like in 6600 6 occurs twice..it will be counted like this ;right?
the explanation given is :from the unit's place to the hundred's place there are 27000 digits in all.6 would appear in a tenth of these nos. i.e. 2700. In the thousand's place it appears 1000 times. Hence in all 3700.
but i didnt understand this..kindly some1 explain!!!!
Ok I realized my mistake....
It will come 1000 times in the thousand's place as I mentioned
but it will come 300*9 = 2700 times from 1000 to 9999...I counted additional 300 for the 1st 1000 numbers also...
So the ans will be b
the answer given is (b)3700
n i had a doubt..like in 6600 6 occurs twice..it will be counted like this ;right?
the explanation given is :from the unit's place to the hundred's place there are 27000 digits in all.6 would appear in a tenth of these nos. i.e. 2700. In the thousand's place it appears 1000 times. Hence in all 3700.
but i didnt understand this..kindly some1 explain!!!!
Ya in 6600 you have to count 6 twice....
Wat I get from the explanation is that if you leave the hundred's digit and only consider last 3 places i.e. units tens and hundred's then the no of digits in the range 1000-9999 are which lie in these 3 places are:
9000*3 = 27000
9000 bcoz there are 9000 no.s in the range 1000-9999
3 bcoz of the 3 places we r considering
Now each of these 3 places consists of 10 digits (0-9) equally....Hence 6 will come 1/10th times i.e. 2700 times...
and again 1000 times in the thousand's place....
So that makes it 3700....
Hi All. Can anyone here help me out with the following:
The charges of a taxi journey are decided on the basis of the distance convered and the amount of the waiting time during a journey. Distance wise, for the first 2kms (or any part thereof) of a journey, the metre reading is fixed at Rs.10(if there's no waiting). Also, if a taxi is boarded and it doesnot move, then the metre reading is again fixed at Rs. 10 for the first tem minutes of waiting. For every additional kilometre the metre reading changes by Rs. 5(with changes in the metre reading being in multiples of Re.1 for every 200mts. travelled). for every additional minute of waiting, the metre reading changes by re.1 (no account is taken of a fraction of a minute waited for or of a distance less than 200 mts. travelled). The net metre reading is a function of the amount of time waited for and the distance travelled.
The cost of running a taxi depends on the fuel efficiency (in terms of milege/litre), depreciation (straight line over 10 years) and the driver's salary (not taken into account if the taxi is self owned).
Depreciation is Rs. 100 per day everyday of the first 10 years. This depreciation has to be added equally to the cost for every customer while calculating the profit for a particular trip. Similarly, the driver's daily salary is also apportioned equally across the customers of the particular day. Assume, for simplicity, that there are 50 customers every day (unless otherwise mentioned). The cost of fuel is Rs. 15 per litre (unless otherwise stated).
The customer has to pay 20% over the metre reading while settling his bill. Also assume that there is no fuel cost for waiting time (unless otherwise stated).
If Preetpal Singh's taxi is 14years old and has a fuel efficiency of 12km/litre of fuel, find his profit in a run from Howrah Station to Park Street ( a distance of 7kms) if the stoppage time is 8mins. (Assume he owns the taxi). Also find his %age profit.
Would appreciate if someone can elaborate his/her answer as well.
Hi All. Can anyone here help me out with the following:
The charges of a taxi journey are decided on the basis of the distance convered and the amount of the waiting time during a journey. Distance wise, for the first 2kms (or any part thereof) of a journey, the metre reading is fixed at Rs.10(if there's no waiting). Also, if a taxi is boarded and it doesnot move, then the metre reading is again fixed at Rs. 10 for the first tem minutes of waiting. For every additional kilometre the metre reading changes by Rs. 5(with changes in the metre reading being in multiples of Re.1 for every 200mts. travelled). for every additional minute of waiting, the metre reading changes by re.1 (no account is taken of a fraction of a minute waited for or of a distance less than 200 mts. travelled). The net metre reading is a function of the amount of time waited for and the distance travelled.
The cost of running a taxi depends on the fuel efficiency (in terms of milege/litre), depreciation (straight line over 10 years) and the driver's salary (not taken into account if the taxi is self owned).
Depreciation is Rs. 100 per day everyday of the first 10 years. This depreciation has to be added equally to the cost for every customer while calculating the profit for a particular trip. Similarly, the driver's daily salary is also apportioned equally across the customers of the particular day. Assume, for simplicity, that there are 50 customers every day (unless otherwise mentioned). The cost of fuel is Rs. 15 per litre (unless otherwise stated).
The customer has to pay 20% over the metre reading while settling his bill. Also assume that there is no fuel cost for waiting time (unless otherwise stated).
If Preetpal Singh's taxi is 14years old and has a fuel efficiency of 12km/litre of fuel, find his profit in a run from Howrah Station to Park Street ( a distance of 7kms) if the stoppage time is 8mins. (Assume he owns the taxi). Also find his %age profit.
Would appreciate if someone can elaborate his/her answer as well.
Since, taxi 14yrs old so no deprciation & self owned so no salary issue
cost is only incurred by fuel.
For one trip fuel consumed= 7/12litre
cost=7/12*15=Rs. 35/4 for every trip
Meter reading for one trip=10+5*5+8*1=Rs.43
Total amt given by customer=1.2*43
profit=1.2*43-35/4=Rs.42.85
%profit=42.85/35/4=489%
My answer for this one comes out to (c). But Arun SHarma it's given as (a)
Percentages LOD II
Ques 35. Reema goes to a shop to buy a radio costing Rs.2568. The rate of sales tax is 7% and the final value is rounded off to the next higher integer. She tells the shopkeeper to reduce the price of the radio so that she has to pay Rs. 2568 inclusive of sales tax. Find the reduction needed in the price of the radio.
(a)Rs. 180(b)Rs.210(c)Rs.168(d)None of these
My answer for this one comes out to (c). But Arun SHarma it's given as (a)
Percentages LOD II
Ques 35. Reema goes to a shop to buy a radio costing Rs.2568. The rate of sales tax is 7% and the final value is rounded off to the next higher integer. She tells the shopkeeper to reduce the price of the radio so that she has to pay Rs. 2568 inclusive of sales tax. Find the reduction needed in the price of the radio.
(a)Rs. 180 (b)Rs.210 (c)Rs.168 (d)None of these
The ans will be a)
The final value she will have to pay is = 1.07*2568 = 2748(after rounding off)
After the reduction she will have to pay = 2568...
Diff = 2748 - 2568 = 180...
Since, taxi 14yrs old so no deprciation & self owned so no salary issue
cost is only incurred by fuel.
For one trip fuel consumed= 7/12litre
cost=7/12*15=Rs. 35/4 for every trip
Meter reading for one trip=10+5*5+8*1=Rs.43
Total amt given by customer=1.2*43
profit=1.2*43-35/4=Rs.42.85
%profit=42.85/35/4=489%
Hi Gaurishankar:
Many thanks for your reply. Taking this a step ahead, how would depreciation would have been included in the solution had the taxi been 9 years old and also was not self owned. Would addition of 100 as depreciation solved the problem? and how would salary of the driver be equally apportioned? Kindly advise.
Hi Gaurishankar:
Many thanks for your reply. Taking this a step ahead, how would depreciation would have been included in the solution had the taxi been 9 years old and also was not self owned. Would addition of 100 as depreciation solved the problem? and how would salary of the driver be equally apportioned? Kindly advise.
If the taxi been 9 yrs old then there must be some more data like cost of the taxi would have been given, suppose taxi cost is Rs. 10000, then depreciation would hav been valid upto 10000/100 months ie 100 months or , 8 yrs & 4 months or so on. If the taxi lesser old than 8.4 months then for evry day u hav to include depreciation for 1 day ie 100/30=3.33rs. for older taxi there is not cost incurred by taxi.
Also, for salary it has nothing to do with the customer. while calculating profit u hav to just calculate salary for one day by dividing total salary by 30. Also for one trip profit some extra data is required like no. of trips etc. so that every day salary can be equally apportioned to each trip.