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June 23, 2019

Question 1

20

21

22

23

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The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e. at 12 o'clock). ==> The hands coincide 22 times in a day.

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Question 2

32 8/11min

36 5/11min

90min

96min

55 min. spaces are covered in 60 min. 60 min spaces are covered in (60/55 × 60)min = 65 5/11 min Loss in 64 min = ( 65 5/11- 64 ) = 16/11 min Loss in 24 hrs = ( 16/11 × 1/64 × 24 × 60 ) min = 32 8/11 min

Question 3

144º

150º

168º

180º

Angle traced by the hour hand in 6 hours = ( 360/12 × 11/3 )degrees =180º

Question 4

58 1/2º

64º

67 1/2º

72 1/2º

Angle traced by hour hand in 21/4 hrs = ( 360/12 × 21/4)º = 157 1/2º Angle traced by min. hand in 15min. = ( 360/12 × 15 )º = 90º. Required angle = ( 157 1/2 )º - 90º = 67 1/2º

Question 5

Friday

Sunday

Thursday

Saturday

15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947) Odd days in 1600 years = 0 Odd days in 300 years = 1 46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day Jan. Feb. Mar. Apr. May. Jun. Jul. Aug ( 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 ) = 227 days = (32 weeks + 3 days) = 3 odd days. Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days. Hence, as the number of odd days = 5 , given day is Friday.

Question 6

Tuesday

Monday

Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday.

Question 7

Wednesday

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Question 8

16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776) Counting of odd days : 1600 years have 0 odd day. 100 years have 5 odd days. 75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days 1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day. Jan Feb Mar Apr May Jun Jul 31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 2 days) Total number of odd days = (0 + 2) = 2. Required day was 'Tuesday'.

Question 9

28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006) Odd days in 1600 years = 0 Odd days in 400 years = 0 5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days (31[jan] + 28 [Feb]+ 31[Mar] + 30[April] + 28[May] ) = 148 days 148 days = (21 weeks + 1 day) 1 odd day. Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day. Given day is Sunday

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