Problem Solving

By walking ¾ of his usual speed, a man reaches his office 15 minutes late. What is his usual time in eons, if one eon is equivalent to ¾ hours?
(A) ½
(B) ¾
(C) 1
(D) 1 ¼
(E) 1 ¾

Usual speed of man=x

d=distance from man's starting point to office

t is in hours

d/x=t

d/(3x/4)=t+1/4

4t/3=t+1/4

t/3=1/4

t=3/4

# of eons=3/4/(3/4)=1

C

sanju09 wrote:By walking ¾ of his usual speed, a man reaches his office 15 minutes late. What is his usual time in eons, if one eon is equivalent to ¾ hours?
(A) ½
(B) ¾
(C) 1
(D) 1 ¼
(E) 1 ¾

I like fractions and percentages !!!!


Concept applied :

Suppose, A * B is a constant K.

if A increases by 25%, B has to decrease by 20% to give K.

in other words,

1/4th increase A - > 1/5th decrease in B

Similarly,
1/5th increase A - > 1/6th decrease in B

and
1/3rd increase A - > 1/4th decrease in B

see the pattern?

Solution:

we are given : decreasing speed by 1/4th, increases the time by 15 mins.

but from the above pattern, 1/4th decrease in one variable results in 1/3rd increase in other variable.

therefore, 1/3rd of total time is 15 mins. Total time is 45 mins.

Eon is 3/4 of an hour. which is again 45 mins.
[spoiler]
hence total time is One eon. IMO C. [/spoiler]

Great solutions guys!

Here's another one:

total distance = D
Speed = S

D / (3/4S) - D/ S= 1/4 ----> D/T=3/4 Thus normally it takes him 3/4 hour to complete a trip.

Answer is clearly C!

harshavardhanc wrote:

sanju09 wrote:By walking ¾ of his usual speed, a man reaches his office 15 minutes late. What is his usual time in eons, if one eon is equivalent to ¾ hours?
(A) ½
(B) ¾
(C) 1
(D) 1 ¼
(E) 1 ¾

I like fractions and percentages !!!!


Concept applied :

Suppose, A * B is a constant K.

if A increases by 25%, B has to decrease by 20% to give K.

in other words,

1/4th increase A - > 1/5th decrease in B

Similarly,
1/5th increase A - > 1/6th decrease in B

and
1/3rd increase A - > 1/4th decrease in B

see the pattern?

Solution:

we are given : decreasing speed by 1/4th, increases the time by 15 mins.

but from the above pattern, 1/4th decrease in one variable results in 1/3rd increase in other variable.

therefore, 1/3rd of total time is 15 mins. Total time is 45 mins.

Eon is 3/4 of an hour. which is again 45 mins.
[spoiler]
hence total time is One eon. IMO C. [/spoiler]

Wow!! What a pattern!!! Can we take it home for a laboratory test?

sanju09 wrote: Wow!! What a pattern!!! Can we take it home for a laboratory test?

sure!! it's all yours !!!

would like to see what you do with it !

harshavardhanc wrote:

sanju09 wrote: Wow!! What a pattern!!! Can we take it home for a laboratory test?

sure!! it's all yours !!!

would like to see what you do with it !

don't worry, I am gentleman

sanju09 wrote:

harshavardhanc wrote:

sanju09 wrote: Wow!! What a pattern!!! Can we take it home for a laboratory test?

sure!! it's all yours !!!

would like to see what you do with it !

don't worry, I am gentleman

never did I say, you are not !

harshavardhanc wrote:

sanju09 wrote:

harshavardhanc wrote:

sanju09 wrote: Wow!! What a pattern!!! Can we take it home for a laboratory test?

sure!! it's all yours !!!

would like to see what you do with it !

don't worry, I am gentleman

never did I say, you are not !

Let's communally thank our amended constitution for men started having faith in men now!!

sanju09 wrote:By walking ¾ of his usual speed, a man reaches his office 15 minutes late. What is his usual time in eons, if one eon is equivalent to ¾ hours?
(A) ½ (B) ¾ (C) 1 (D) 1 ¼ (E) 1 ¾

Normal speed = 4x km/hrs and time taken = t hrs
3/4 of usual speed = 3x
Dist = Speed x Time
4x* t = 3x*( t+15) divide by x
t = 45min = 1 eon
IMO C