Problem on Numbers

[THUSSU]

Originally Posted by koolfriend4u

A group of friends went on a holiday to a hill station. It rained for 13 days. But when it
rained in the morning, the afternoon was lovely. And when it rained in the afternoon, the
day was preceded by clear morning.
Altogether there were 11 very nice mornings and 12 very nice afternoons. How many days did
their holiday last?

Let the number of total mornings be M and the number of total afternoons be E
The wet mornings must be M-11 and the horrid afternoons are E-12
So, M-11+E-12=13 or M+E = 36
but M+E is one day so the number of days must be 18!

[koolfriend4u]

Originally Posted by koolfriend4u

Which of the following day(s) can't be the last day of a century? Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.

Ans:
easiest one.

The last day of a century can not be Tuesday, Thursday or Saturday.
( hope everybody aware of calendar probs. 5317 - fri,wed,mon,sun alone be the last days of centuries)

Here it goes.

A normal year has 365 days whereas a leap year has 366 days. Every year which is divisible by 4 is called a leap year.
Also, every 4th century is a leap year but no other century is a leap year.
1 normal year = 365 days = 52 weeks + 1 day
1 leap year = 366 days = 52 weeks + 2 day

Thus, a normal year has 1 odd day whereas a leap year has 2 odd days.
100 years = 76 normal years + 24 leap years = 76*[52 weeks + 1 day] + 24*[52 weeks + 2 day] = (76*52) weeks + 76 days + (24*52) weeks + 48 days = 5200 weeks + 124 days = 5217 weeks + 5 days

i.e. 100 years contain 5 odd days
Similarly, 200 years contain 10 odd days
i.e. 3 odd days. 300 years contain 15 odd days
i.e. 1 odd days.

400 years contain (20+1) odd days i.e. 0 odd days.

Note that 400 years contain one more leap year.

Also, we have Sunday for 0 odd day, Monday for 1 odd day, Tuesday for 2 odd days, and so on... Thus, last day of first century is Friday. (5 odd days) Last day of second century is Wednesday. (3 odd days) Last day of third century is Monday. (1 odd days)
Last day of forth century is Sunday. (0 odd days)

Since the order is repeating in successive cycles, the last day of a century can not be Tuesday, Thursday or Saturday.

[koolfriend4u]

A ship went on a voyage.
After it had travelled 180 miles a plane statrted with 10 times the speed of the ship.
Find the distance when they meet from starting point.

[whocarez]

200 miles

[koolfriend4u]

Originally Posted by whocarez

200 miles

200 miles

Let's say the ship is travelling v mi/hr
and plane took t hours to meet the ship

Than, vt is the distance ship travelled after plane started
(10v)t = 10vt is the distance plane travelled.

So we have, vt + 180 = 10vt
or 9vt = 180
or vt = 20

Hence distance ==> 180 + 20 = 200 miles


But.... one more soln. with me.

By the time the plane flies 180 miles the ship would have travelled 18 miles.

180 + 18 = 198 miles

By the time the plane flies 18 miles the ship would have travelled 1.8 miles.

198 + 1.8 = 199.8 miles

By the time the plane flies 1.8 miles the ship would have travelled .18 miles.

199.8 + .18 = 199.98 miles

By the time the plane flies .18 miles the ship would have travelled .018 miles.

199.98 + .018 = 199.998 miles

By the time the plane flies .018 miles the ship would have travelled .0018 miles.

199.998 + .0018 = 199.9988

And so on, assuming the plane never tries to overtake the ship

[mizzou]

speeds x and 10 x
rel dis = 180
rel speed = 10x - x = 9x
time = 180/9x = 20/x

Ans = Dis Travelled by plane = 10x * 20/x = 200 miles

[koolfriend4u]

smart work mizzou.

[koolfriend4u]

An orange glass has orange juice and white glass has apple juice both of equal volumes. 50ml of the orange juice is taken and poured into the apple juice. 50ml from the white glass is poured into the orange glass. Of the two quantities, the amount of apple juice in the orange glass and the amount of orange juice in the white glass, which one is greater and by how much?

[koolfriend4u]

soln. equal in amnt.

[koolfriend4u]

There are some chicken in a poultry. They are fed with corn. One sack of corn will come for 9 days. The farmer decides to sell some chicken and wanted to hold 12 chicken with him. He cuts the feed by 10% and sack of corn comes for 30 days. So initially how many chicken are there?

There is an element which triplicates in every hour. Each of these 3
items inturn reproduce exactly 3 other items. If a single compund is kept in a
container at noon and the container is full by midnight. After how many hours is the container 1/3 full.

100 Kg. Potatoes with 98% water content are dried in an oven. The percentage of water decreases to 50 %. What is the weight of potatoes now.

There are n Railway stations. Ticket facility is 10available between every
two stations. Recently, m new stations are bulit so that 42 new tickets
are to be printed. How many stations were there? How many are newly
constructed.