Math's Magic's

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Math's Magic's

1. What was the day of the week on 17th June, 1998?

A.Monday

B.Tuesday

C. Wednesday

D. Thursday

Answer : C. Wednesday

Explanation:-

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)

Odd days in 1600 years = 0

Odd days in 300 years = (5 x 3) 1

97 years has 24 leap years + 73 ordinary years.

Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.

Jan.  Feb.   March    April    May      June 

(31 +  28  +  31   +   30   +   31   +   17) = 168 days

168 days = 24 weeks = 0 odd day.

Total number of odd days = (0 + 1 + 2 + 0) = 3.

Given day is Wednesday.

2.On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?

A.Sunday

B.Thursday

D.Tuesday

C.Friday

Answer : D. Friday

Explanation :-

The year 2006 is an ordinary year. So, it has 1 odd day.

So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.

But, 8th Dec, 2007 is Saturday.

8th Dec, 2006 is Friday.

3.January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?

A.Monday

B.Tuesday

C.Wednesday

D.Sunday

Answer :- B. Tuesday

Explanation :-

The year 2007 is an ordinary year. So, it has 1 odd day.

1st day of the year 2007 was Monday.

1st day of the year 2008 will be 1 day beyond Monday.

Hence, it will be Tuesday.

4. A takes 5 days to complete a job and B takes 10 days to complete the same job. In how much time will they complete the job together?

A.2 Days

B.2.33 Days

C.3 Days

D.3.33 Days

Answer :- D. 3.33 Days

Explanation:-

A's efficiency = 20%, B's efficiency = 10%. If they work together they can do 30% of the job in a day. To complete the job they need 3.33 days. 

5. 4 men and 6 women working together can complete the work within 10 days. 3 men and 7 women working together will complete the same work within 8 days. In how many days 10 women will complete this work?

A. 4 Days

B.5 Days

C. 6 Days

D. 7 Days

Answer:- B. 5 Days

Explanation:-

 Let number of men =x, number of women = y

⇒ Efficiency of 4 men and 6 women = 100/10 = 10%

⇒ so, 4x+6y = 10

Above equation means 4 men and 6 women can do 10% of the job in one day.

⇒ Efficiency of 3 men and 7 women = 100/8 = 12.5%

so, 3x+7y = 12.5

By solving both equations we get, x = -0.5 and y = 2

⇒ Efficiency of 1 woman(y) = 2% per day

⇒ Efficiency of 10 women per day = 20%

So 10 women can complete the job in 100/20 = 5 days

6.If 20 persons can do a piece of work in 7 days, then calculate the number of persons required to complete the work in 28 days.

A.5

B.10

C.15

D.25

Answer :- A. 5

Explanation:-

Number of persons × days = work.

20 × 7 = 140 man-days.

Now, X × 28 = 140 man-days.

→ X = 5

Therefore, in second case the required number of person is 5.

Short Tricks

Since, work in constant, therefore

M1×D1 = M2×D2 = Work done

20 × 7 = M2 × 28 → M2 = 5.

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