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In the recent past in Kolkata, abduction of primary-school children, which was unheard of before, suddenly was on the rise. The Police Commissioner of Kolkata IPS Mr Vineet Kumar Goyal, instructed all the schools in Kolkata to take steps to increase the security of their students during the school hours.

St Xavier’s School, Kolkata, already had a security system in place. However, the management, after a survey, decided to beef up the security at Gate D on Short Street, which was rather a secluded area. The management took the decision that there must be two guards guarding Gate D each day of the week from Monday to Saturday. The security agency they did business with sent five top security guards named Ambar, Biplab, Chandan, Dinesh and Ekram for the job. 

However, they had some constraints while performing their duty :

a) None of the guards worked for three consecutive days in a week

b) Ambar did not work on Monday, Tuesday, and Wednesday

c) Biplab and Dinesh both had a service gun, and hence never worked on the same day

d) Biplab worked on alternate days and he worked with Ambar on Friday

e) Ekram worked for the maximum number of days in a week amongst all the five guards

f) Both Biplab and Dinesh worked for an odd number of days during the week

g) Two particular guards out of the five worked for the same number of days in a week

h) Each of the rest three guards worked for a distinct number of days

Question :

If Ekram worked with one particular guard twice during a week, then which guard worked on the same day as Dinesh ?

 

 

Option: 1

Chandan

 


Option: 2

Ekram


Option: 3

 Ambar

 


Option: 4

Cannot be determined


Answers (1)

best_answer

There are in total 6*2 = 12 guard shifts required. 

That can be only fulfilled along with all the constraints given if Ekram does 4 shifts, Biplab does 3 shifts, Ambar and Chandan does 2 each, and Dinesh does 1 shift, as 4+3+2+2+1 = 12

Given below are all the possible situations of shift combinations.

The left hand table A represents Ekram working with one particular guard twice a week, and there are two possible cases which satisfy all the constraints

The right hand table B represents Ekram working with a different guard every time during the week, and here too there are two possible cases which satisfy all the constraints  

 

A

Case 1 

Case 2

Monday

Biplab, Ekram

Biplab, Ekram

Tuesday

Dinesh, Chandan

Dinesh, Chandan

Wednesday

Biplab, Ekram

Biplab, Ekram

Thursday

Ekram, Chandan

Ambar, Ekram 

Friday

Ambar, Biplab

Ambar, Biplab

Saturday

Ambar, Ekram 

Ekram, Chandan
     

B

Case 1 

Case 2

Monday

Biplab, Ekram

Biplab, Ekram

Tuesday

Ekram, Chandan/Dinesh

Ekram, Chandan/Dinesh

Wednesday

Biplab, Chandan

Biplab, Chandan

Thursday

Ambar, Ekram 

Ekram, Chandan/Dinesh

Friday

Ambar, Biplab

Ambar, Biplab

Saturday

Ekram, Chandan/Dinesh

Ambar, Ekram 

Hence, from Table A, which represents Ekram working with one particular guard twice a week, Chandan works on the same day as Dinesh in either of the two possible cases.
 

Posted by

HARSH KANKARIA

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