## pls solve them...

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• hi pls help me in solving these problems.. 1. how many 3 digit no.s r there which when divided by 7 or 8 gives a remainder of 4 in each case? 2. what is the
Message 1 of 5 , Jun 16, 2006
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hi pls help me in solving these problems..

1. how many 3 digit no.s r there which when divided by 7 or 8 gives a remainder of 4 in each case?

2. what is the sum of all the numbers formed by taking each of the digits 2,3,5,6 and 8 once?

3.fresh mango contains 70% water by weight whereas dry mango contains 10% water by weight. what is the weight of dry mango that can b obtained from 20 kg of fresh mango?
a. 6.66kg
b. 6 kg
c. 6.84 kg
d. cannot b determined

4. starting with 1, positive integers are written one after the other. what is the 40000th digit that will be written?
a. 2
b. 4
c. 3
d. 1

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• Ans 1 . Such a no. will be LCM(7,8)*K + 4 where K is a +ve integer i.e. 56K + 4 so for 3 digits 1
Message 2 of 5 , Jul 2, 2006
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Ans 1 .
Such a no. will be LCM(7,8)*K + 4  where K is a +ve integer
i.e. 56K + 4
so for 3 digits  1<K<18
16 values of K are possible . Hence 16 such nos.....

Ans 2.
there will be 5*4*3*2*1 = 120  nos. that can be formed with these 5 digits....
lets consider the no. which end with '1'.....
ie. fix '1' at the end so there are 4! such nos.....similarly for 2,3,4,5....
hence the sum of the unit's digits of these nos ....
24*(1+2+3+4+5)
the sum of the ten's digits of these nos ....
24*(1+2+3+4+5)*10
the sum of the hundred's digits of these nos ....
24*(1+2+3+4+5)*100
the sum of the thousand's digits of these nos ....
24*(1+2+3+4+5)*1000
the sum of the ten thousand's digits of these nos ....
24*(1+2+3+4+5)*10000
total sum = 24 * (1+2+3+4+5)* (10000+1000+100+10+1)
= 24 * (1+2+3+4+5)* (11111)
= 24 * (15)* (11111)
= 4! * (15)* (11111)
so, in general , we have a formula for this type of questions ....
ie. SUM = (total digits-1)! * (sum of digits) * (1111.......)
where no. of 1's = total digits

Ans 3.
20 kg of fresh mango ---> 6 Kg net mango :)
so to contain this much net mango
we get to know that 6kg should be 90% of the dry mango...
so .9X = 6
X = 6.66

Ans. 4
m workin on it :)

shruti bhagi <shruti_bhagi@...> wrote:
hi pls help me in solving these problems..

1. how many 3 digit no.s r there which when divided by 7 or 8 gives a remainder of 4 in each case?

2. what is the sum of all the numbers formed by taking each of the digits 2,3,5,6 and 8 once?

3.fresh mango contains 70% water by weight whereas dry mango contains 10% water by weight. what is the weight of dry mango that can b obtained from 20 kg of fresh mango?
a. 6.66kg
b. 6 kg
c. 6.84 kg
d. cannot b determined

4. starting with 1, positive integers are written one after the other. what is the 40000th digit that will be written?
a. 2
b. 4
c. 3
d. 1

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• soln 1 ... 3 digit nos which divided by 7 leaves remainder four is 7x+4 where x=14 to 142 so total (142-14)+1 nos=129 3 digit nos which divided by 8 leaves
Message 3 of 5 , Jul 3, 2006
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soln 1
---------------------------------------
3 digit nos which divided by 7 leaves remainder four is 7x+4 where x=14 to 142 so  total (142-14)+1 nos=129
3 digit nos which divided by 8 leaves remainder four is 8x+4 where x=12 to 124
so total (124-12)+1nos=113

so total no of nos is=129+113=242
but there r nos that when divided by both 7 n 8 leave reamainder 4. We have counted thse nos twice

these nos rof the form 56x+4 where x=2 to 17 total 17-2+1 nos=16
So actual no of 3 digit nos =242-16=226

soln 2
-------------------------
its a very standard problem u can get in any XI th standard maths book

soln 4
---------------------------------------
Digits contributed by 1 digit nos=1*9
Digits contributed by  2 digit nos=2*90
Digits contributed by 3 digit nos=3*900
.
.
.
.
Digits contributed by n digit nos=n*9*10^(n-1)
----------------------------------------------------------------
Total no of digits= n*10^n- (10^n-1)/9
putting n=4
we find total no of digits upto all 4 digit nos is 38,889
No of digits after 4 digit nos and 40,000 th digit is
1111
all r contributed by 5 digit nos
there r 200 5 digit nos
so 40,000th digit is the staring digit of 10200 i.e 1

Ans (d)

shruti bhagi <shruti_bhagi@...> wrote:
hi pls help me in solving these problems..

1. how many 3 digit no.s r there which when divided by 7 or 8 gives a remainder of 4 in each case?

2. what is the sum of all the numbers formed by taking each of the digits 2,3,5,6 and 8 once?

3.fresh mango contains 70% water by weight whereas dry mango contains 10% water by weight. what is the weight of dry mango that can b obtained from 20 kg of fresh mango?
a. 6.66kg
b. 6 kg
c. 6.84 kg
d. cannot b determined

4. starting with 1, positive integers are written one after the other. what is the 40000th digit that will be written?
a. 2
b. 4
c. 3
d. 1

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Nibedita Moitra

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• answer to the 1st question: there are 16 numbers. solution: to find least no. which when divided by 7 and 8 leaves remainder 4 in each case, find lcm of 7 and
Message 4 of 5 , Jul 8, 2006
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there are 16 numbers.
solution:

to find least no. which when divided by 7 and 8 leaves remainder 4 in
each case, find lcm of 7 and 8 and add 4 to it i.e. (lcm of 7 & 8 )+
4.

but we need 3 digit nos.
so lcm of 7 nd 8 is 56. the lowest three digit multiple of 56 is 112
(56*2).
therefore, the first three digit number which gives 4 when divided by
either 7 or 8 is 112+4 i.e. 116.

similarly the highest three digit no. fulfilling the condition would
be the highest three digit multiple of 56 + 4.
the highest three digit no. which is a multiple of 56 is 952 (to find
out divide 1000 by 56 which gives 17.something. so 17*56 will be the
highest three digit multiple of 56.)

so 952+4 = 956 is the highest three digit number fulfilling the
criteria.

therefore by A.P. a+(n-1)d = L
now, L=952
a=116
d=56

hence, n=16.

--- In ascent4cat@yahoogroups.com, shruti bhagi <shruti_bhagi@...>
wrote:
>
> hi pls help me in solving these problems..
>
> 1. how many 3 digit no.s r there which when divided by 7 or 8
gives a remainder of 4 in each case?
>
> 2. what is the sum of all the numbers formed by taking each of
the digits 2,3,5,6 and 8 once?
>
> 3.fresh mango contains 70% water by weight whereas dry mango
contains 10% water by weight. what is the weight of dry mango that
can b obtained from 20 kg of fresh mango?
> a. 6.66kg
> b. 6 kg
> c. 6.84 kg
> d. cannot b determined
>
> 4. starting with 1, positive integers are written one after the
other. what is the 40000th digit that will be written?
> a. 2
> b. 4
> c. 3
> d. 1
>
>
> ---------------------------------
> Sneak preview the all-new Yahoo.com. It's not radically different.
>
• ... the answer s 1.. coz u see that there are 9 1 digit numbers and 90 2 digit numbers and 900 three digit nums.. so keep on going .. ull end up as 1.. hey can
Message 5 of 5 , Jul 17, 2006
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>
> 4. starting with 1, positive integers are written
> one after the other. what is the 40000th digit that
> will be written?
> a. 2
> b. 4
> c. 3
> d. 1
>

the answer s 1.. coz u see that there are 9 1 digit
numbers and 90 2 digit numbers and 900 three digit
nums.. so keep on going .. ull end up as 1..

hey can anyone tell me how to improve english grammar
and RCS...

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