Dear Reader, Below you can find three questions of moderate difficulty level. These are similar type of questions with slight variations between the questions.
Final year students (ECE) of Excellent Engineering College wanted to celebrate their placement in a leading IT company on a pay package of Rs.3.6 lakhs per annum. They went to the nearby restaurant. None of them was having a credit card or debit card. When the bill for Rs.2000 came it was seen that two friends had not brought money with them.This resulted in the other members contributing Rs.50 more than what they would have paid if the two friends had brought sufficient money. Find the number of students who went to the restaurant?
a) 8 b) 10 c) 12 d) 16
Answer : b) 10
Let P be the number of person who went to the restaurant
They have to pay a total of Rs. 2000
Each person should have paid Rs. 2000/P
But two of them could not pay. Hence deficit amount = Amount to be paid by each person x 2 persons = (2000/P) x 2 = 4000/P ...(1)
The remaining people had to pay extra amount of Rs. 50 each.
Therefore, Extra amount actually paid by remaining people = (P - 2 persons ) x 50 ...(2)
Above calculated extra amount should be equal to the deficit created when two persons failed to pay. Therefore, values of (1) and (2) should be equal
(P - 2) 50 = 4000/P
P (P-2) = 4000/ 50
P2 - 2P = 80
P2 - 2P - 80 = 0
For Factorizing, think of the two number with a difference of 2 and the product is 80 i.e the number 10 and 8 which satisfies the above condition.
P2- 10 P + 8P - 80 = 0
P(P – 10) + 8 (P -10) = 0
(P+8) (P – 10) = 0
Either P = -8 or + 10. But P cannot be negative because number of students cannot be a negative number.
Therefore, P = 10
12 employees of an Information Technology company in Bengaluru wanted to arrange for a pleasure trip to nearby place. Originally the cost of the trip was estimated at Rs. 6000. Few people could not make it up in the last minute so each participating member had to pay Rs. 100 more than the amount they would have paid earlier. How many members went to trip ?
a) 10 b)12 c) 14 d) 16
Answer : a) 10
12 People initially planned to go for a trip. Since the total cost was estimated to be 6000, each would had planned to pay Rs. 6000/12 = Rs. 500.
Let number of people who missed to attend the trip be M.
Then deficit amount would had been Number of people who didn't attend x Amount planned per person = M x 500 = 500M ...(1)
Extra amount paid by remaining members = Rs. 100 x Number of people who attended = 100 x (12 - M) ...(2)
The deficit amount should be equal to the extra amount paid
Therefore, values of (1) and (2) will be same,
i.e 500M = 100(12 - M)
600 M = 1200
Or M = 2
Number of people who went to trip = Total planned members - M = 12 - 2 = 10
A grand party was arranged for 15 employees of a multi national bank as a mark of finalization of books of accounts as on March 31, 2012. A certain sum of money was estimated for party spend and it was agreed to share the expenses amongst members. But unfortunately three employees could not make it up, others who participated had to pay Rs.300 more than the amount they would have paid if all those agreed attend the party. What was the total amount estimated for party spend ?
a. 18000 b. 16000 c. 3600 d. 36000
Answer : a. 18000
Let A be the net amount planned for the party.
Since there were 15 members, initial planned amount per person would be A/15
Three employees were unable to attend the party. Hence the deficit in amount would be 3 persons X amount planned per person = 3 x A/15 = A/5 ...(1)
Remaining members paid extra amount of Rs. 300 each to make up for the deficit created.
Hence net extra amount paid would be Number of attending persons X 300 = (15 - 3) X 300 = Rs. 3600 ...(2)
But the deficit amount should be equal to the net extra paid by attending members.
Therefore, values of (1) and (2) should be equal,
i.e A/5 = 3600 Or A = 18000
Therefore, amount estimated for party spend = Rs. 18000