A,B,C and D play a game of cards. A says to B "If I give you 8 cards, you will have as many as C has and I shall have 3 less than what C has. Also if I take 6 cards from C, I shall have twice as many as D has". If B and D together have 50 cards, how many cards has A got?
Answer: D B + 8 = C.
A - 8 = C - 3.
A + 6 = 2D.
B + D = 50.
solving these we get A = 40.
Q. No. 14:
In a objective examination of 90 questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attempting all the 90 questions a students got a total of 387 marks. Find the number of questions that he attempted wrong.
Answer: A Let the wrong questions be x. We get the equations (90-x)*5 - x*2 = 387 => x=9
Q. No. 15:
Large, medium and small ships are used to bring water. 4 large ships carry as much water as 7 small ships. 3 medium ships carry the same amount of water as large ship and 1 small ship, 15 large, 7 medium and 14 small ships, each made 36 journey and brought a certain quantity of water. In how many journey would 12 large, 14 medium and 21 small ships bring the same quantity?
Answer: B Ratio of large, medium and small = 7:6:4 so, numbers of journeys => (15*7 + 7*6 + 14*4)36 / (12*7 + 14*6 + 21*4) = 7308/252 = 29.
Q. No. 16:
A,B,C and D each had some money. D doubled the amounts with the others. C then doubled the amounts with the others. B then doubled the amounts with the others. A then doubled the amounts with the others. At this stage, each of them has Rs 80. Find the initial amount with C (in Rs).
Answer: D Before doubling, the amounts B,C and D, each of them must have had 80/2 = Rs 40. A must have then had Rs 80+ Rs 120 = Rs 200. Similarly, we can work out the amounts with each of them before the other doubled the amounts. The results are summarized below:- Finally -------------------> A(80), B(80), C(80), D(80) Before A doubles--------->A(200), B(40), C(40), D(40) Before B doubles--------->A(100), B(180), C(20), D(20) Before C doubles--------->A(50), B(90), C(170), D(10) Before D doubles--------->A(25), B(45), C(85), D(165)
Q. No. 17:
A person starting with 64 rupees and making 6 bets, wins three times and loses three times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is
A :
a gain of Rs 27
B :
a loss of Rs 37
C :
neither gain nor a loss
D :
a gain or a loss depending upon the order in which the wins and losses occur.
Answer: B As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order). The overall resultant will remain same. So final amount with the person will be (in all cases) 65(1.5)(1.5)(1.5)(0.5)(0.5)(0.5) = Rs 27. Hence the final result is a loss of Rs 37.
Q. No. 18:
21 pencils and 29 pens cost Rs 79. But if the number of pencils and pens were interchanged, the cost would have reduced by Rs 8. Find the cost of each pen.