Directions (1-4): Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
1. What is the rate of interest p.c.p.a.?
I. An amount doubles itself in 5 years on simple interest.
II. Difference between the compound interest and the simple interest earned on a certain amount in 2 years is Rs. 400.
III. Simple interest earned per annum is Rs. 2000.
- 1)I & II only
- 2)II and III only
- 3)I only
- 4)All I, II and III
- 5)I only or II and III only
Ans: (5)
I.(P× r× 5)/100 = P , r= 20
II.P(1+r/100)^2 –P- (P×r×2)/100= 400; Pr^2 =4000000.
III.(P×r×1)/100= 2000; Pr= 200000
From II and III
Pr^2 ÷ Pr = 20; r=20
So Answer can be given by either I only or II and III only.
2. What is the percent profit earned by the shopkeeper on selling the articles in his shop?
I. Labelled price of the articles sold was 130% of the cost price.
II.Cost price of each article was Rs. 550.
III. A discount of 10% on labelled price was offered.
- 1)Only I
- 2)Only II and III
- 3)Only I and III
- 4)All I,II and III
- 5) Can’t be answered with I, II and III
Ans: (3)
I. Let C.P. be Rs. x.
Then, M.P. = 130% of x = Rs. 13x/10
III. S.P. = 90% of M.P.
Thus, I and III give, S.P. = Rs. (90/100)x(13x/10)= Rs.117x/100
Gain = Rs.(117x/100)- x = Rs.17x/100
Thus, from I and III, gain % can be obtained.
Clearly, II is redundant.
3. What is the length of a running train P crossing another running train Q?
I.These two trains take 18 seconds to cross each other.
II.These trains are running in opposite directions.
III.The length of the train Q is 180 metres.
- 1)I only
- 2)II and III only
- 3)I and III only
- 4)All I,II and III only
- 5)Can’t be answered with I, II and III.
Ans: (5)
Let the length of the train P be x metres.
II. These trains are running in opposite directions.
III. Length of the train Q is 180 m.
I. Time taken by P to cross Q =(180 + x)/ Relative Speed
(180 + x)/ Relative speed = 18
Thus, even with I, II and III, the answer cannot be obtained.
4. How many marks did Tarun secure in English?
I. The average mark obtained by Tarun in four subjects including English is 60.
II. The total marks obtained by him in English and Mathematics together are 170.
III. The total marks obtained by him in Mathematics and Science together are 180.
- 1)I and II only
- 2)II and III only
- 3)I and III only
- 4)All I, II and III.
- 5)None of these .
Ans: (5)
From I, total marks in 4 subjects = (60 x 4) = 240.
From II, E + M = 170
From III, M + S = 180
All Obtion are not true so None of these is the current Ans.
5. Prashant invested a certain sum at simple interest & Vikram invested same sum at compound interest. The ratio of rates (in % per annum) of simple and compound interest is 2:1. After 2 year two of them receive equal amounts, then at what rate did Vikram invest ?
- 1)50 %
- 2)100 %
- 3)150%
- 4)200 %
- 5)Can’t be Determined.
Ans: (4)
Let rate which invested by Prashant : rate which invested by vikram = 2x:x
(P*2x*2)/100 = P[(1+x/100)^2-1]
By solving this , we get x=200%
So rate at which Vikram invested = 200%
6. In a school there are total of 50 students in class X, who are divided in three sections A, B and C. Section A and B have equal no. of students. All the students of the class wrote a test. The average marks obtained by the section A and B together is 52.5. The average marks obtained by the section A and C together is 60. The average marks obtained by the section B and C together is 70. The average marks obtained by the students of sections A, B and C together is 60. How many Students are there in Section C.
- 1)10
- 2)15
- 3)20
- 4)Can’t be determined
- 5)None of these
Ans: (1)
Let the no. of students in A, B and C is a, a,and c.
Let the marks obtained by A , B and C is x,y and z.
Average of marks by class A and B= 52.5
(x+y)/2a = 52.5
Same as …(y+z)/(a+c)= 60
(x+z)/(a+c)=70
(x+y+z)/(a+a+c)= 60
On solving this a=2c
total no. of students =50
2a+c=50
So c=10.
7. A group consists of m equally efficient workers. A piece of work was started by one of them. The p’th worker (where 2 less than or equal to p less than or equal to m) joined the work (p-1)x days after the (p-1)’th worker joined The work was completed in mx days after the m’th worker joined. The 1’st worker received a share of Rs.5500 out of total Rs. 38500 paid to the group for completing the work . Find m ?
- 1)8
- 2)9
- 3)10
- 4)11
- 5) None of these
Ans: (3)
Time taken to complete the work = x+ 2x+3x+4x+…..+(p-1)x+….mx= mx(m+1)/2
Let the work done by each worker per day be k units.
Total Work=work done by 1’st worker+ work done by 2’nd worker +…..+ work done by m’th worker .
=k(x+2x+3x+…+mx)+k(2x+3x+4x+…+mx)+k(3x+4x+5x+…+mx)+….+kmx
= k(x)+ k2(2x)+k3(3x)+…..+km(mx)
= kx(1+2^2+3^2+….+m^2)
Part of total wages obtain by 1st worker = {kxm(m+1)/2}/ {kxm(m+1)(2m+1)/6)
= 5500/ 38500
3/(2m+1)= 55/385 ;
m=10.
8. A car travelled a distance of 900 km. it developed an engine problem after travelling of Some distance. It travelled remaining distance at 3/5th of its speed.it reached 2 hours late.if the engine problem had developed after it had travelled for another 150 km. it would have reached 1 hour late than the time it actually reached . Find the distance it travelled without any problem and its speed over that part of journey (in km, kmph)
- 1)500 , 100
- 2) 600, 100
- 3) 500 150
- 4) 600, 150
- 5) None of these
Ans: (2)
Let the engine problem happen at x km Distance and speed over entire part of journey is s km/hr.
x/s + (900-x) / (3x/5) = 900/s+ 2 ------eqn(1)
(x+150)/s + 900-(x+150) /(3x/5) = 900/s +1 --------eqn(2)
Eqn(2)- Eqn(1)
x= 600 km and speed s= 100km/hr
9. The price of radio at the beginning of a year was Rs. 3000. It increased by x % and then decreased by y % over the year. It increased by x % and then decreased by y % over the next year too. At the end of the second year, the price of radio was Rs. 3000. Which of the following can be true ?
- 1) x>y
- 2) x=y
- 3) x<y
- 4) none of these
- 5) None of these
Ans: (1)
Price of radio at the end of 1st year = 3000(1+x/100)(1-y/100)
Price of it at the end of next year = 3000(1+x/100)(1-y/100)(1+x/100)(1-y/100).
It is also 3000.
so taking obtion consideration when x=y then so price = 3000(1+y/100)^2(1-y/100)^2 which is less than 3000
So for it to be equal x>y.
10. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
- 1) 3/91
- 2) 1/22
- 3) 5/24
- 4) 2/91
- 5) 3/24
Ans: (4)
5c3/15c3 = 2/91
11. Two partners invested Rs. 1250 and Rs.850 respectively in a business. Both the partners distribute 60% of profit equally and distribute the rest 40% as the interest of their capitals .If one partner received Rs. 30 than other.Find the total Profit .
- 1)Rs. 400
- 2)Rs. 375.84
- 3)Rs. 393.75
- 4)Rs. 380.25
- 5)None of these
Ans: (3)
A’s 40% profit / B’s 40 % profit = 1250/850 = 25/17
Using componendo & Dividendo
40% profit of A and B / 30 = 42/8
So total profit = 42/8 *30*(100/40)= Rs. 393.75
12. If the circumference of one circle is 5/2 times that of other , how many times the area of smaller circle is the bigger one ?
- 1)4/25
- 2)25/24
- 3)25/4
- 4)24/25
- 5) None of these
Ans: (3)
Ratio of circumference = 5/2
So ratio of area = (5/2)^2 = 25/4
13. If (p/q)-(q/p)=21/10 then what is the value of(4p/q)+(4q/p) ?
- 1)58/5
- 2)59/5
- 3)121/105
- 4)21/105
- 5)105/121
Ans: (1)
Let p/q=a then q/p=1/a
a -(1/a)=21/10
a=5/2
=>4(5/2)+4(2/5)
(20/2)+(8/5)
(100+16)/10
=>58/5
14. A tank has a leak, which would empty it in 8 hours. A tap is turned on which fills at the rate of 4 liters per minute and the tank is now emptied in 12 hours. Find the capacity of the tank.
- 1)5670 lit
- 2)5760 lit
- 3)6570 lit
- 4)6750 lit
- 5)None of these
Ans: (2)
1/8 * 1/x = 1/12
solving we get,
x = 24
so total capacity is, 24*4*60 = 5760 lt..
In 1 minute a tap fill the tank 4 litre
so,in 8 hours=(8*60)minute=480 minute a tap fill the tank (480*4)=1920 litre.
according to question 1920 litre will be emptied in 8 hours.
so,in 12 hours it will be emptied 2880 litre.
again,the tap fill the tank 4 litre in 1 minute.
so,in 12 hours=720 minutes the tap fill the tank (720*4)=2880 litre
so,according to question as the two works(filling the tank & empty the tank) are going on in 12 hours,so the capacity of the tank=(2880+2880)litre=5760litre
15. By Selling a article for Rs. 8260, A merchant has a profit of 18%, but due to fall of demand he sell at only 2/3 of the profit %. Find the new Selling Price.
- 1)7000
- 2)7500
- 3)7800
- 4)7840
- 5) None of these
Ans: (4)
New Selling price = (8260*112) /118 = 7840