Number System

[dazed]

Originally Posted by sharulgoel

please give a detailed solution..i dont know the correct answer will find it out
but if u got the answer then plz share the solution too.
thanks

I thin the ans is 666.
Two appraoches can be used
1) 1212121212...3000 digits = N
reprsenting in form of coprinmes
N=37*k1 = 27* k2 + 18
Solving this for k2=24, we get N=666.

2) 1212121212... 300 digits can be written as
=12121212(297 digit)*1000 + 212 mod 999
=12121212(297 digit)*(999+1) + 212 mod 999
=12121212(297 digit)*1 + 212 mod 999
=12121212(294 digit)*1000 + 121 + 212 mod 999
=12121212(294 digit)*(999+1) + 121 + 212 mod 999
= ......
( 121 + 212 ) * 50 mod 999 = 666.

[sharulgoel]

Originally Posted by dazed

I thin the ans is 666.
Two appraoches can be used
1) 1212121212...3000 digits = N
reprsenting in form of coprinmes
N=37*k1 = 27* k2 + 18
Solving this for k2=24, we get N=666.

2) 1212121212... 300 digits can be written as
=12121212(297 digit)*1000 + 212 mod 999
=12121212(297 digit)*(999+1) + 212 mod 999
=12121212(297 digit)*1 + 212 mod 999
=12121212(294 digit)*1000 + 121 + 212 mod 999
=12121212(294 digit)*(999+1) + 121 + 212 mod 999
= ......
( 121 + 212 ) * 50 mod 999 = 666.

Thanks Gr88

Next Question:

The sum of 16 natural nos is 900. What is the minimum value of the LCM of these no.s???

[dazed]

Originally Posted by sharulgoel

Thanks Gr88

Next Question:

The sum of 16 natural nos is 900. What is the minimum value of the LCM of these no.s???

I guess we need to assume all nubmers equal here
but since 16x=900, wont give a integral value of x.
we take 15x=900

x=60
14 numbers - 60 each and 15th number- 30 and 16th number-30
LCM - 60.
If options are there, we can check if any other smaller options are there.

[prateek7563]

PLease solve the questions using ALLIGATIONS only:

1. A sum of Rs36.90 is made up of 90 coins that are either 20p or 50 p. Find out no. of 20 p coins.

2. A mixture of 20L of brandy and water contains 10% water. how much water shall be added to make water 25% of mixture?

[masoom]

Originally Posted by prateek7563

PLease solve the questions using ALLIGATIONS only:

1. A sum of Rs36.90 is made up of 90 coins that are either 20p or 50 p. Find out no. of 20 p coins.

2. A mixture of 20L of brandy and water contains 10% water. how much water shall be added to make water 25% of mixture?

for second i can suggest a method...

20 v
10 % 100%
25 %
75 % 15 %

so 20/v= 75/15..

getting v= 4 from here..

[prakharc]

Originally Posted by prateek7563

PLease solve the questions using ALLIGATIONS only:

1. A sum of Rs36.90 is made up of 90 coins that are either 20p or 50 p. Find out no. of 20 p coins.

2. A mixture of 20L of brandy and water contains 10% water. how much water shall be added to make water 25% of mixture?

For 1) Rs 36.90 from 90 coins so each coin= 41p

Now 50 p coins=x .... 90 p coins= 90-x ...such that resultant= 41p per coin

x/(90-x)=(41-20)/(50-41)=7/3 => x=63

So 63 50p coins and 27 20p coins

[prateek7563]

A mixture of 20L of brandy and water contains 10% water. how much water shall be added to make water 25% of mixture?

Solve using alligations only!!!

[prakharc]

Originally Posted by prateek7563

A mixture of 20L of brandy and water contains 10% water. how much water shall be added to make water 25% of mixture?

Solve using alligations only!!!

Let water=x

so 20/x = (100-25)/(25-10) => x= 4 litres

So 4 litre of water shd be added

[prateek7563]

Solve using alligation only:
1. If a man decides to travel 80Km in 8hrs partly by foot and partly by bicycle.His speed by foot being 8km/h and that by bicycle being 16km/h,what distance is travelled by foot?

2. A bag contains a total of 105 coins of rs1,50p,25p. find total no. of 1rs coins if there are rs50.5 in bag and it is known that number of 25p coins is 133.33% more than the number of 1rs coins.

[masoom]

Originally Posted by prateek7563

Solve using alligation only:
1. If a man decides to travel 80Km in 8hrs partly by foot and partly by bicycle.His speed by foot being 8km/h and that by bicycle being 16km/h,what distance is travelled by foot?

2. A bag contains a total of 105 coins of rs1,50p,25p. find total no. of 1rs coins if there are rs50.5 in bag and it is known that number of 25p coins is 133.33% more than the number of 1rs coins.

first one is :

let he travel by foot x km... so on bicycle he walked 80-x km..

now average speed...

so {x/80-x}= ( 16-10) /( 10-...

x/80-x = 3..

so x=60km..

he walked 60 km on foot