Page 242 - Services Selection Board (SSB) Interviews
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238 Clocks
Answer with Solution
Concept Applicator
1. (c) At 6 : 30 A.M. from the formula here P = 6 and Hence they will be opposite to each other at 3 : 49
Q = 30 so required angle is 11 × 30/2 – 30 × 6 = minute : 0.09 second
165 – 180 = – 15 or ignoring the negative sign the 8. (d) Consider exactly at 4 : 00, minute hand is at
required angle is 15° position ‘12’ and hour hand is at ‘4’ hence angle
2. (a) At 11 : 50 A.M. from the formula here P = 11 between these two hands at 4 : 00 is 120°.
and Q = 50 so required angle is 11 × 50/2 – 30 × Since relative speed between them is 11/2° per
11 = 275 – 330 = – 55 or ignoring the negative sign minute or every minute the minute hand will travel
the required angle is 55° 11/2° more than the hour hand.
3. (a) At 4 : 20 A.M. from the formula here P = 4 and They will be perpendicular to each other when the
Q = 20 so required angle is 11 × 20/2 – 30 × 4 = minute hand will travel (120 – 90 =) 30° more than
110 – 120 = – 10 or ignoring the negative sign the the hour hand. And time taken for this is (30)/(11/2)
required angle is 10° = 60/11 or 5 5/11 minute.
4. (b) At 1 : 40 from the formula here P = 1 and Q = Hence they will be perpendicular to each other at 4 :
40 so required angle is 11 × 40/2 – 30 × 1 = 220 – 11 minute : 45.45 second
30 = 190 the required angle is 190°
9. (c) Consider exactly at 9 : 00, minute hand is at
5. (a) At 10 : 10 from the formula here P = 10 and Q position ‘12’ and hour hand is at ‘9’ hence angle
= 10 so required angle is 11 × 10/2 – 30 × 10 = between these two hands at 9 : 00 is 270°.
55 – 300 = – 245 the required angle is 245°
Since relative speed between them is 11/2° per
6. (a) Consider exactly at 3 : 00, minute hand is at minute or every minute the minute hand will travel
position ‘12’ and hour hand is at ‘3’ hence angle 11/2° more than the hour hand.
between these two hands at 3 : 00 is 90°. They will be together when the minute hand will
Since relative speed between them is 11/2° per travel 270° more than the hour hand. And time
minute or every minute the minute hand will travel taken for this is (270)/(11/2) = 540/11 or 49 1/11
11/2° more than the hour hand. minute.
They will be together when the minute hand will Hence they will be opposite to each other at 9 : 49
travel 90° more than the hour hand. And time taken minute : 0.09 second
for this is (90)/(11/2) = 180/11 or 16 4/11 minute. 10. (c) Consider exactly at 9 : 00, minute hand is at
Hence they will coincide at 3 : 16 minute : 21.81 position ‘12’ and hour hand is at ‘9’ hence angle
second between these two hands at 9 : 00 is 270°.
7. (c) Consider exactly at 3 : 00, minute hand is at Since relative speed between them is 11/2° per
position ‘12’ and hour hand is at ‘3’ hence angle minute or every minute the minute hand will travel
between these two hands at 3 : 00 is 90°. 11/2° more than the hour hand.
Since relative speed between them is 11/2° per They will be together when the minute hand will
minute or every minute the minute hand will travel travel (270 – 180 =) 90° more than the hour hand.
11/2° more than the hour hand. And time taken for this is (90)/(11/2) = 180/11 or 16
They will be opposite to each other when the minute 4/11 minute.
hand will travel (90 + 180 =) 270° more than the Hence they will be opposite to each other at 9 : 49
hour hand. And time taken for this is (270)/(11/2) = minute : 21.81 second
540/11 or 49 1/11 minute.
