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On the occasion of Janmasthmi, four persons – A1, A2, A3 and A4 bought certain dozens of bananas for their respective houses. Their wives also went to the market and bought bananas. Further it is known that

I. The wives are W1, W2, W3 and W4

II. A1 bought as many bananas as his wife, A2 bought twice as many as his wife, A3 bought three times as many as his wife, and A4 bought four times as his wife.

III. W1 bought 2 dozens bananas, W2 bought 3, W3 and W4 bought 4 and 5 dozens of bananas respectively.

IV. The four couples bought 44 dozen of bananas between them.

Which two husbands bought the same number of bananas?

Option 1 -

A2 and A4

Option 2 -

A2 and A1

Option 3 -

A1 and A3

Option 4 -

A4 and A1

1 View | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Payal Gupta | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

Let us denote, the dozens of Bananas bought by A4's wife by a1, a2 by A3's wife, a3 by A2's wife and a4 by A1's wife. We prepare the table given below Bananas bought:

A1 = a₄ A1's wife = a₄

A2 = 2a₃ A2's wife = a₃

A3 = 3a₂ A3's wife = a₂

A4 = 4a₁ A4's wife = a₁

Where (a1, a2, a3, a4) is a rearrangement of (2, 3, 4, 5). Now, (a4 + 2a3 + 3a2 + 4a1) + (a4 + a3 + a2 + a1) = 44 4a1 + 3a2 + 2a3 + a4 = 44 – (2 + 3 + 4 + 5) = 30 …. (1) (Sum a1 + a2 +

...more

<div>Let us denote, the dozens of Bananas bought by A4's wife by a1, a2 by A3's wife, a3 by A2's wife and a4 by A1's wife. We prepare the table given below Bananas bought:A1 = a4               A1's wife = a4A2 = 2a3             A2's wife = a3A3 = 3a2             A3's wife = a2A4 = 4a1             A4's wife = a1Where (a1, a2, a3, a4) is a rearrangement of (2, 3, 4, 5). Now, (a4 + 2a3 + 3a2 + 4a1) + (a4 + a3 + a2 + a1) = 44 4a1 + 3a2 + 2a3 + a4 = 44 – (2 + 3 + 4 + 5) = 30 …. (1) (Sum a1 + a2 + a3 + a4 = 2 + 3 + 4 + 5)Now, we have to find the dozens a1, a2, a3, a4 satisfying (1) and also that (a1, a2, a3, a4) is a rearrangement of (2, 3, 4, 5)Let a1 = b1 a1 + a2 = b2a1 + a2 + a3 = b3Then, (1) becomesa1 + (a1 + a2) + (a1 + a2 + a3) + (a1 + a2 + a3 + a4) = 30b1 + b2 + b3 = 30 – 14 = 16b1 = a1 belongs to (2, 3, 4, 5)b2 = a1 + a2 belongs to (5, 6, 7, 8). Obtained by taking sum of any two dozens of set (2, 3, 4, 5)b3 = a1 + a2 + a3 belongs to (9, 10, 11, 12) obtained by taking sum of all possible 3 dozens collections of the set (2, 3, 4, 5)So, we see that b1 + b2 + b3 = 16 is obtained by</div>Combination b1 = 2, b2 = 5, b3 = 9 Consequently, a1 = 2a1 + a2 = 5 a2 = 3a1 + a2 + a3 = 9 a3 = 4a1 = 2, a2 = 3, a3 = 4Then, a4 = (a1 + a2 + a3 + a4) – (a1+ a2 + a3) = 14 – 9 = 5A4's wife bought 2 Bananas, she is W1. A3's wife bought 3 Bananas, she is W2. A2's wife bought 4 Bananas, she is W3. A1's wife bought 5 Bananas, she is W4.

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There were ten events in the last years “annual cultural festival” of xyz international College. Following guidelines have been issued to schedule the “annual cultural festival”:

I. A college board has organized the ten events Z1, Z2, Z3, Z4, Z5, Z6, Z7, Z8, Z9, Z10 on six days of week with holiday on Sunday; not having more than two events on any of the days.

II. Event begins on Wednesday with event Z6.

III. Z4 is accompanied by some other event but not on Thursday. Z1 and Z7 are on the same day immediately after the holiday.

IV. There is only event on the last day and Saturday. Z2 is immediately followed by Z8, which is immediately followed by Z9.

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Which of the following events is scheduled on the last day?

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B1, B2, B3, B4, B5, B6 and B7 are brothers. Two brothers had an argument and B1 said to B2, “you are as old as B3 was when I was twice as old as B4, and will be as old as B5 was when he was as old as B3 is now”. B2 said to B1, “You may be older than B6 but B7 is as old as I was when you were as old as B7 is, and B4 will be as old as B6 was when B6 will be as old as B7 is”.

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From the 1st statement: B2 is now as old as B3 was in the past. Hence B2 is younger to B3 or B2 < B3. Also sometime in the past B1 was twice as old as B4. So B1 is elder to B4 or B1 > B4. B3 will be as old as B5 in future, hence B3 < B5. The second statement suggests: B1 > B6. B1 was as old as B7 in the past. Hence B1 > B7. B4 will be as old as B6 in future. Hence B6 > B4. B6 will be as old as B7 now in future. Hence B7 > B6. B7 was as old as B2, when B1 was as old as B7. Hence B1 = B2. Combining both the results, we get: and B5 > B3 > B2 = B1 > B7 > B6 > B4 (Note by B1 = B2, it is meant that they are of similar age group, not necessarily the same).

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Arun, Ajit, Rohan, Gajraj, Ronit, Shubham, Sweety and Lovely are eight students in a class. Three of them belongs to Kerala and Goa each and two of them belongs to Delhi. Each one of them has a different height. The tallest does not belongs to Delhi and the shortest does not belongs to Kerala. Shubham is taller than Arun and Gajraj but shorter than Lovely and Ajit. Ronit, who does not belongs to Kerala, is taller than Ajit and is second to the tallest. Sweety is shorter than Gajraj but taller than Arun. Lovely who is the fourth from the top belongs to Goa with Gajraj. Sweety does not belong to either Kerala or Delhi. Ajit does not belong to Delhi.

Who is the tallest?

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According to the information provided following arrangement will be obtained:

(K→ Kerala ; G → Goa ; D → Delhi)

Order according to height								Student	Belong
1	2	3	4	5	6	7	8		K	G	D
×	×	×	×	×	×	×	√	Arun	×	×	√
×	×	√	×	×	×	×	×	Ajit	√	×	×
√	×	×	×	×	×	×	×	Rohan	√	×	×
×	×	×	×	×	√	×	×	Gajraj	×	√	×
×	√	×	×	×	×	×	×	Ronit	×	×	√
×	×	×	×	√	×	×	×	Shubham	√	×	×
×	×	×	×	×	×	√	×	Sweety	×	√	×
×	×	×	√	×	×	×	×	Lovely	×	√	×

Six friends Jyoti, Talwar, Rubi, Zahid, Victor and Samson live in the same building. The building has six different floors. Each of them belongs to different states viz., Delhi, Kerala, Manipur, Rajasthan, Tripura, Bihar & no two of them live in same states or floor.

I. One of the friends who live on the fourth floor saw Rubi going up the staircase.

II. Jyoti and Victor did not belong to Tripura.

III. Person who belongs to Kerala lives on the fourth floor.

IV. Samson belongs to Bihar. He didn’t live on the first floor.

V. Talwar lives on the sixth floor, but didn’t belong to Delhi.

VI. Person who belongs to Manipur lives on the second floor. Jyoti and Zahid did not belong to Manipur.

Talwar lives on which of the following floors?

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Looking at the table given in the first question of the set, we get that Talwar lives on the sixth floor.

I. One of the friends who live on the fourth floor saw Rubi going up the staircase.

II. Jyoti and Victor did not belong to Tripura.

III. Person who belongs to Kerala lives on the fourth floor.

IV. Samson belongs to Bihar. He didn’t live on the first floor.

V. Talwar lives on the sixth floor, but didn’t belong to Delhi.

VI. Person who belongs to Manipur lives on the second floor. Jyoti and Zahid did not belong to Manipur.

Which states does Rubi belong to?

Payal Gupta

The data available is not enough to determine where Rubi belongs to. The given data is insufficient to answer the above question.

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