# Aptitude - Clock - Discussion

Discussion Forum : Clock - General Questions (Q.No. 6)
6.
At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
5 min. past 7
 5 2 min. past 7 11
 5 3 min. past 7 11
 5 5 min. past 7 11
Explanation:

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.

At 7 o'clock, they are 25 min. spaces apart.

Minute hand will have to gain only 5 min. spaces.

55 min. spaces are gained in 60 min.

 5 min. spaces are gained in 60 x 5 min = 5 5 min. 55 11

 Required time = 5 5 min. past 7. 11

Discussion:
68 comments Page 1 of 7.

Harish udupa s said:   8 years ago
At 7o clock hour, the hand will be 210 degrees, at 5min minute hand will be 30 degrees, (same line).

So consider 5min 5/11 for hour hand and just 5/11min for minute hand.

For every 1min hour hand rotates by 0.5 degrees so for 60/11 min it rotates by 30/11 degree.

For every min minute hand rotates by 6 degrees for 5/11 min it rotates by 30/11 degree hence equal.

So at 7 past 5min 5/11 it will be 210+30/11 degree in hour hand and 30+30/11 for minute hand difference is 180 degree thus they are in same line.

@amit:11/2min-30h this formula applicable only when h<6
if u put h=6 or above then the min>60 which is not acceptable(for the 180 degree),
in this problem if we put that formula then the ans is 77(10/11)
but in that case the h=7 so we apply the another formula which is 30h-11/2
in this case if we put that then formula the ans is 5(5/11)
if u apply that formula then u will find that min<60 which is acceptable

BASICALLY WE NEED THIS 2 FORMULAS BUT IN DIFF CASE...
hope u will understand:)

Harish udupa s said:   8 years ago
Angle = |11/2 * min-30 * hr| as said by someone.

Where || indicates take positive value.

How is this derived?

=> For every hour, hour hand rotates by 30 degrees (360/12 = 30).

=> For every minute, minute hand rotates by 6 degrees (360/60 = 6).

=> But for every minute, hour hand rotates by 1/2 degree (1 hr = 30 degrees 1 min = half degree).

=> So effective angle = (6 * min) - ((30 * hr) + (0.5 * min)).

=> Solving angle = 5.5 * min - 30 * hour.

Rohit Joshi said:   6 months ago
As the clocks are in a straight line but not together, the angle formed by the hands of the clock will be 180.

Now, We know that Angle = |30*Hours - 11/2*Minutes|
Therefore, 180 = 30*7 * 11/2 * Minutes.
210 - 180 = 11/2 * Minutes.
30 = 11/2 * Minutes.
60/11 = Minutes.
55 * 5/11 = Minutes.
So, finally, the answer is D.
(5)

Mohit Sharma said:   3 years ago
Î¸ = { hour * 30 } diff { min * 11/2 } take difference between greater value and smaller value.

Now for the straight line, we know Î¸ = 180.

We can put all these values in the formula

Hour = 7
Î¸ = 180
min = ?

Î¸ = hour * 30 diff min * 11/2.
180 = { 7 * 30 } diff { min* 11/2}.
180 = { 210 } diff { min* 11/2},
min = 2/11 * 210-180,
min = 60/11.

which is equal to 5 5/11.
(3)

Himanshu dewaangan said:   1 decade ago
ANOTHER METHOD:
In 7 o'clock there are angle between hands= 5*30=150 degree
we have to make that angle = 180 degree
let after X min
min hand will increase angle by = X*6 =6X,on 150 degree

1 degree of min = 1/12 degree of hr
6X degree of min = 6X/12 = X/2 degree of hr (decrease angle on 150)
so angle have to be between hands=180
150+6X-X/2=180
x=5+5/11
ANS=(5+5/11) minute and 7 past

Prasanna said:   8 years ago
Here, is some Equation:

Angle between hands = [(Hour Hand * 30) + (Minute hand * 1/2)] - Minute hand * 6.

(Hour Hand * 30) -> Because At 1 o'clock it will be 30 deg so at 7 it will be 150 deg.

Minute hand * 1/2 -> Hour hand moves 1/2 deg per min.

Minute hand * 6 -> Minute hand moves 6 deg per min.

180 = [7 * 30 + x/2] - 6x.

So, the answer is 5 5/1.

Bangya said:   4 years ago
Assume that the time is 1 O'clock. If we look in a clockwise direction, it's 55 min space but if we look in the anticlockwise direction, it's 5-minute space. Can somebody explain which direction should we look to know the correct minute space?

If both directions are correct, then 5-minute space will be equal to 55-minute space.

Rajendra Sahu said:   1 decade ago
For straight line angle =180
The formula is for finding angle =30H-(11/2)*M
where H =>Hours
M => Minute.
Now

30H-(11/2)*M=180
30*7-(11/2)*M=180
210 - (11/2)*M=180
-(11/2)*M=180-210
-(11/2)*M=-30
11*M=60 (Cross Multiply)
M=60/11 minutes
means 5+5/11 minute

So Time will be

(5+5/11) minute and 7 past