Clock Reasoning Formula with Examples for SSC and Bank Exams

Clock Reasoning Formula with Examples:

EX.6. At what time between 5.30 and 6 will the hands of a clock be at right angles?

$$(A)\ 43{7\over11}min. past \ 5$$

$$(B)\ 43{5\over11}min. past \ 5 $$

$$(C) \ 45 \ min. past 5 $$

$$(D) \ 40 \ min. past \ 7 $$

Explanation:

At 5 o'clock, the hands are 25 min. spaces apart.

To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

55 min. spaces are gained in 60 min.

40 min. spaces are gained in $$\left({60\over55}× 40 \right)min= 43{7\over11}$$

$$ ∴ Required \ time \ = 43{7\over11} \ min \ .past \ 5 $$

EX.7. At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?

$$(A)\ 5{2\over11}min. past \ 7 $$

$$(B)\ 5 \ min. past\ 7 $$

$$(C)\ 5{5\over11}min. past \ 7. $$

$$(D)\ 5{3\over11}min. past \ 7 $$

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   $$\left({60\over55}× 5 \right)min= 5{5\over11}.$$

$$ ∴ Required \ time \ = 5{5\over11} \ min \ .past 7. $$

EX.8. At 3:40, the hour hand and the minute hand of a clock form an angle of:

(A) 125⁰

(B) 120⁰

(C) 135⁰

(D) 130⁰

Explanation:

Angle traced by hour hand in 12 hrs. = 360°.

Angle traced by it in $$ {11\over 3}hrs = \left({360\over12}× {11\over 3} \right)^0 = 110^0 $$

Angle traced by minute hand in 60 min. = 360°.

Angle traced by it in 40 min. =$$ \left({360\over60}× 40 \right)^0 = 240^0 $$

∴ Required angle (240 - 110)° = 130°

EX.9. At what angle the hands of a clock are inclined at 15 minutes past 5?

$$(A) \ 64^0$$

$$(B) \ 58{1\over2}^0 $$

$$(C) \ 72{1\over2}^0 $$

$$(D) \ 67{1\over2}^0 $$

Explanation:

Angle traced by hour hand in $$ {21\over4 }hrs = \left({360\over12}× {21\over4} \right)^0 = 157{1^0\over2}  $$

Angle traced by min. hand in 15 min. = $$ \left({360\over60}× 15 \right)^0 = 90^0 $$

$$ ∴ Required \ angle = \left(157{1\over2} \right)^0 - 90^0 = 67{1^0\over 2} $$

EX.10. The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

(A) 10⁰

(B) 0⁰

(C) 20⁰

(D) 5⁰

Explanation:

Angle traced by hour hand in $$ {13\over3}hrs = \left({360\over12}×{360\over12}   \right)^0 = 130^0$$

Angle traced by min. hand in 20 min. = $$ 20 \ min = \left({360\over60}×20 \right)^0 = 120^0 $$

∴ Required angle = (130 - 120)° = 10°