# Two women were selling marbles int the market place -- 1 at 3 for a paise and other at 2 for a paise. one day both of them were obliged to return home when each had 30 marbles unsold. they put together the 2 lots of marbles and handling them over to a friend asked her to sell them at 5 for 2 paise.now they were expecting to get 25 paise for the marbles as they would have got if sold separately but much to their surprise they go only 24 paise in total.where did the 1 paise go ? can anyone explain the mystery?

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#### Anthony Yekula

• Nov 21st, 2006

Lets assume that two woman?s as A&B

It has given A has 30 marbles and B has 30 marbles

If they given to friend to sell 5 marbles for 2 paise than

60=12*5 i..e  12*2 = 24 paise

But if they sell separately

1)      A sells 3 marbles for 1 paise so

30=10*3 i..e  10*1=10 paise

1) B sells 2 marbles for 1 paise so

30=15*2 i.e 15*1=15 paise

combing A&B gives you 10+15=25

#### John

• Nov 21st, 2006

What's the point?

#### sankar

• Dec 4th, 2006

the above is only explanation

due to combination it will give 1 paise difference thats all

#### Rathinavelu

• Dec 14th, 2006

First women : 3 marbles per paise, then she would have sold 10 sets of marbles(cheap marble)

Second women: 2 marbles per paise, then she would have sold 15 sets of marbles(costlier marble)

When the two types of marbles were combined, we got 60 marbles, 5 marbles per 2 paise. No of sets would be 12 sets.

As you can see, after selling 10 sets the cheapest marbles will be over. the remaining 2 sets i.e 10 marbles will be of costlier kind.

Till the 10 sets the combination is 3 cheap + 2 costlier

Now after selling 10 sets, 2 costlier + 2 coslier + 1 coslier makes a set

the cost of this combination should be 1 paise + 1 paise + 1/2 paise =  2 1/2 paise.

But the women sold this combination also for 2 paise, that is why we got 1 paise difference

#### santosh_kumar0009 Profile Answers by santosh_kumar0009 Questions by santosh_kumar0009

• Dec 14th, 2006

The problem is so simple......:-)

Total number of the unsoled marbels are.. 60

cost is 5 marbles for 2 paise..

there will be 12 sets...

12*2 is 24 paise is the final income...

But there will be 12(3 & 2) set of each marbles=12 set(5) of combined marbels.

cost of total of 36 cheaper marbel and 24 costlier marbels is 24

But there are only 30 cheaper and 30 costlier.

After 10 set of 5 marbels only costlier marbels are left..

#### ravichandra_r Profile Answers by ravichandra_r

• Dec 19th, 2006

Point is that two women got confused.. thinking this way

each of them were selling at 3 / P and 2 / P and each got equal numbers in their hand i.e 30+30.. so they averaged the sales bye (3+2)/2.. i.e by selling 5 / P they will get same earnings as they original would have got if sold idividually. Their assumption is wrong.. to get same amount the would hv done as below

A's return 30/3 = 10P

B's expected return 30/2 = 15P

A+B's expected return = 25P

Hence they would have fixed the combined price as 60/25 per P i.e 12/5 (i.e 12 per 5P which is 2.4 for every P. However with the averaging confusion they sold at 5/2P which is 2.5 for every P.

Hence while selling they received only 60/2.5 = 24P insted of their expectation of 60/2.4 = 25P

#### veena

• Jan 31st, 2007

1st man has 30 marbles...which he could sell at 1ps for 3 marbles..like 30/3 = 10ps he could get...2nd man also has 30 marbles left....supposed to be sold at 1ps for 2 marbleslike 30/2 = 15ps he could get....So they were gonna get 25ps in totalBut the decide to combine there marbles...30 + 30 = 60 marbles...and sell at the rate of 2ps for 5 marbles60/5 = 12so they will get 12 x 2 = 24pswhat's the mystery??

#### Vairavan

• Feb 28th, 2007

First women : 3 marbles per paise, then she would have sold 10 sets of marbles(cheap marble)

Second women: 2 marbles per paise, then she would have sold 15 sets of marbles(costlier marble)

When the two types of marbles were combined, we got 60 marbles, 5 marbles per 2 paise. No of sets would be 12 sets.

As you can see, after selling 10 sets the cheapest marbles will be over. the remaining 2 sets i.e 10 marbles will be of costlier kind.

Till the 10 sets the combination is 3 cheap + 2 costlier

Now after selling 10 sets, 2 costlier + 2 coslier + 1 coslier makes a set

the cost of this combination should be 1 paise + 1 paise + 1/2 paise =  2 1/2 paise.

But the women sold this combination also for 2 paise, that is why we got 1 paise difference

#### kiranmai

• Mar 1st, 2007

one women sells 3 marbles for 1 paise

so for 1 marble it costs 1/3 paise

for 30 marbles 1/3*30=10 paisse

second women sells 2 marbles for 1 paise

so for 1 marble 1/2 paise

for 30 marbles 1/2*30=15 paise

totally 10 +15 is 25 paise

but  now they are selling at 5 marbles for 2 paise

so for 1 marble 2/5 paise

for 30+30=60 marble 2/5*60=24 paise

#### welldonehari

• Mar 6th, 2007

hi my dear friend its simple to explain, let me explain for u

x sold 3 marbles per paise so for 30 marbles he got 10 paise
y sold 2 marbles per paise so for 30 marbles he got 15 paise
now when x + y solds 60 marbles such that 5 marbles for 2 paise they got 24 paise here the q is where is that one paise

when 3 marble sold for 1 paise the rate of 1 marble is  0.33333 paise so here u got some loss. (note it is very imp.)

when 2 marbles sold for 1 paise the rateof 1 mable is 0.5 paise

now add x and y the rate of 2 marble(each one from x and y) u got 0.833 paise

instead he sold 5 marbles for 2 paise so the rate of 1 marble is 2/5= 0.4 paise
now for 30 sets i.e. 60 marbles or 12 sets (if 5 marbles per set) there fore now now 0.4*12=4.8 paise(if 5 marbles is for 2 paise) convert it for 1 paise =4.8/2 =2.4 paise

now do u got it

#### vamsi laxman Profile Answers by vamsi laxman

• Dec 11th, 2009

A would have got 10 paise and B would have got 15paise if sold individually. The excess there and the defecit here have been balanced and one paise lost

#### stockball Profile Answers by stockball

• May 24th, 2011

I think they both lost their marbles...

#### Hassan Farooqi

• Jul 18th, 2011

The answer is simple. The women were no mathematicians otherwise they wont be selling marbles :) They calculated the wrong rate. (30+30)*(2/5)=24 whereas 10+15=25. Instead of calculating ((1/3)+(1/2))/2 (0.4166.n) per marble, they calculated (2+3)/(1+1) (0.40) per marble. If they were charging paisas per marbles instead of marbles per paisa, they would not have been confused. Lucky they were not playing hedge funds with out pension money.

#### Muhammed Yazin

• Jun 30th, 2016

Before combined selling
The cost of one marble sold by 1st woman is ₹⅓ and one sold by 2nd woman is ₹. So a group of 5 will actually cost
(5*⅓+5*)/2=25/12
= 2+(1/12)
That means in combined selling every set sold for a price which is ₹1/12 less than the actual price.
Here total 60 marbles sold in 12 sets of 5.
So the total loss is 12x(1/12)=₹1

#### Faizan tintoiya

• Oct 13th, 2016

First of all, 2 marbles for 5 paisa
In this first have 3 marbles and second have 2 marbles.
First women sells 3 marbles for 1 paisa sold out early and second women sells 2 marbles for 1 paisa sold out for rate of 3 marbles for 1 paisa so 1 paisa error  