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  • Directions for question Anirban, Biswajit, Charbak, Dibyendu and Emon were five good friends since their Jadavpur University days, and were hav

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Anirban, Biswajit, Charbak, Dibyendu and Emon were five good friends since their Jadavpur University days, and were having an offshore posting in Manila for M/s CTS for the last few years. They were all Bengalis and shared the same bachelor accommodation in Manila. The CTS South-East Asia Team Head Mr Chatterjee brought them a big earthen pot of rasgullas from Kolkata as a personal gift during his Manila visit on a Saturday. 

They decided to enjoy the delicacy rare for a resident of Manila, on Sunday, an off day for them. They kept the pot in the refrigerator. 

Now, Bengalis inherently have a sweet tooth, and hence are extremely fond of rasgullas. Being young men, they found it extremely difficult to cub their urge to have a taste of the sweet. During the night, at different times, they stealthily raided the refrigerator, without the knowledge of the others, to eat a few of the rasgullas.

Next morning, on the Sunday, during breakfast time the five friends found that only one-eight of the original number of rasgullas remained in the pot. 

It was also known that :

a) Emon ate the rasgullas before Dibyendu did

b) None of them ate more than half the number of rasgullas that were there in the pot when they went to eat it

c) The friend who ate last ate only one-fourth of the rasgullas that were remaining in the pot when he went to eat it

d) Emon ate half of the rasgullas that were left in the pot when he went to eat it

e) Anirban ate the same number of rasgullas as Emon did

f) Dibyendu ate the rasgullas after Charbak did

g) When Anirban went to eat the rasgullas, only four-fifth of the original number of rasgullas were left in the pot

h) When Dibyendu had finished eating, more than one-eight of the original number of rasgullas was left 

Question

Who among the following options ate the maximum number of rasgullas ?

 

Option: 1

Emon

 

 


Option: 2

Dibyendu
 


Option: 3

Charbak

 


Option: 4

Biswajit


Answers (1)

best_answer

From information number (c), the friend who ate last, that is Biswajit, ate only one-fourth of the number of rasgullas that were remaining in the pot. However, after Biswajit had finished, one-eight of the original number of rasgullas remained in the pot. Hence, after Biswajit had finished, three-fourth of the number of rasgullas that were remaining in the pot before he started eating would be left. But that is one-eight of the original number. Thus, the fraction of original number of rasgullas that were remaining in the pot before Biswajit started eating would be (1/8)/(3/4) = 1/6. Also Biswajit had eaten (1/6 – 1/8) = 1/24 of the original number of rasgullas.

As per information (g), fraction of rasgullas left in the pot when Anirban went to eat was four-fifth of the original number. Hence fraction of original number of rasgullas eaten by Charbak was one-fifth.

Let x be the fraction of rasgullas left after Anirban finished eating. As per information (d), the next friend, Emon, ate x/2 of the number of rasgullas. Hence Anirban, who ate the same number, also ate x/2 of the number of rasgullas. 

Thus, we can say that 

4/5 – x/2 = x

or, 3x/2 = 4/5

or, x = 8/15

So, Anirban ate (8/15)/2 = 4/15 of the original number of rasgullas, and so did Emon. Also after Anirban finished eating, 8/15 of the original number of rasgullas was left. Also, after Emon finished eating (8/15 – 4/15) = 4/15 of the original number of rasgullas were left.

Now, the fraction of original number of rasgullas that were remaining in the pot before Biswajit started eating was 1/6. Hence the fraction of original number of rasgullas that were remaining in the pot after Dibyendu had eaten was also 1/6. So Dibyendu ate (4/15 – 1/6) = 1/10

Hence :

Order of eating rasgullas on Saturday night

Fraction before eating

Fraction after eating

Fraction eaten

Charbak

1

4/5

1/5

Anirban

4/5

8/15

4/15

Emon

8/15

4/15

4/15

Dibyendu

4/15

1/6

1/10

Biswajit

1/6

1/8

1/24

 It can be seen that of all the fractions eaten, 4/15 is the largest amount. So both Anirban and Emon ate the maximum number of rasgullas on Saturday night.

Hence, among the given options, Emon ate the maximum number of rasgullas

 

Posted by

HARSH KANKARIA

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