MPPGCL-MPPGENCO Aptitude-Numerical Contributed by Anju updated on Mar 2019

MPPGCL-MPPGENCO Aptitude and Reasoning model questions

1.     Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
A.     57%
B.     60%
C.     65%
D.     90%
Explanation: Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage = (11628/20400 x 100)% = 57%.

2.     What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
A.     1
B.     14
C.     20
D.     21
Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
:. Required percentage = (14/70 x 100)% = 20%.

3.     Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
A.     9
B.     10
C.     12
D.     20
Explanation
: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9 /54 x 60) min = 10 min.

4.     The cost price of a Rs.100 stock at 4 discount, when brokerage is 1/4 % is:
A.     Rs. 95.75
B.     Rs. 96
C.     Rs. 96.25
D.     Rs. 104.25
Explanation
: C.P. = Rs.(100 - 4 + 1/4) = Rs.96.25

5.     The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's discount is:
A.     Rs. 960
B.     Rs. 840
C.     Rs. 1020
D.     Rs. 760

Explanation
: T.D. = (B.G. x 100) /(R x T) = Rs.(270 x 100) / (12 x 3) = Rs.750.
:. B.D. = Rs.(750 + 270) = Rs. 1020.

6.     The banker's discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:
A.     Rs. 360
B.     Rs. 432
C.     Rs. 540
D.     Rs. 1080
Explanation
: Sum = B.D. x T.D. = Rs.72 x 60 = Rs.72 x 60 = Rs.360.
B.D. - T.D.           72 - 60               12

7.     A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
A.     49 m2
B.     50 m2
C.     53.5 m2
D.     55 m2
Explanation
: Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2

8.     The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
A.     8, 20, 28
B.     16, 28, 36
C.     20, 35, 45
D.     None of these
Answer : Option B
Explanation:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
=> 20x = 80
=> x = 4
:. Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

9.    What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
A.     196
B.     630
C.     1260
D.     2520
Explanation:
L.C.M. of 12, 18, 21 30                 2 | 12 - 18 - 21 - 30
----------------------------
= 2 x 3 x 2 x 3 x 7 x 5 = 1260.                              3 | 6 - 9 - 21 - 15
----------------------------
Required number = (1260 ÷ 2)                                   | 2 - 3 - 7 - 5
= 630.

10.     8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 81. How much wine did the cask hold originally?
A.     18 litres
B.     24 litres
C.     32 litres
D.     42 litres
Explanation
: Let the quantity of the wine in the cask originally be x litres.
Then, quantity of wine left in cask after 4 operations = [x (1 - 8/x)4] litres.
:. (x(1- (8/x))4)    =        16
x                     81
=> (1-8/x)4 =    (2/3)4
=> ((x-8)/x) = 2/3
=> 3x - 24 = 2x
=> x = 24

11.     To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
A.     10
B.     35
C.     62.5
D.     Cannot be determined
E.     None of these
Explanation
: Let the capacity of 1 bucket = x.
Then, the capacity of tank = 25x.
New capacity of bucket =       2 x
5
Required number of buckets =  25x    = (25x * 5/2x)
(2x/5)

= 125         = 62.5
2

12.     The value of 489.1375 x 0.0483 x 1.956 is closet to:
0.0873 x 92.581 x 99.749
A.     0.006
B.     0.06
C.     0.6
D.     6
Explanation
:   489.1375 x 0.0483 x 1.956 =     489 x 0.05 x 2
0.0873 x 92.581 x 99.749         0.09 x 93 x 100
=      489
9 x 93 x 10

= 163    x    1
279        10

= 0.58 = 0.058 = 0.06.
10
Direction (for Q.No. 13):  Find out the wrong number in the series.
13.     196, 169, 144, 121, 100, 80, 64
A.     169
B.     144
C.     121
D.     100
E.     80
Explanation:
Numbers must be (14)2, (13)2, (12)2, (11)2, (10)2, (9)2, (8)2. So, 80 is wrong.

14.     The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
A.     69
B.     78
C.     96
D.     Cannot be determined
E.     None of these
Explanation:
Let the ten's digit be x and unit's digit be y.
Then, x + y = 15 and x - y = 3 or y - x = 3.
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6.
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.
So, the number is either 96 or 69.
Hence, the number cannot be determined.

15.     In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
A.     266
B.     5040
C.     11760
D.     86400
E.     None of these
Explanation:
Required number of ways = (8C5 x 10C6)
= (8C3 x 10C4)
=   8 x 7 x 6       x     10 x 9 x 8 x 7
3 x 2 x 1         4 x 3 x 2 x 1

= 11760.

Direction (for Q.No. 16): Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement (s) is / are sufficient to answer the given question. Read the both statements and

Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
Give answer (E) if the data in both Statements I and II together are necessary to answer the question.

16.   Two towns are connected by railway. Can you find the distance between them?
I.      The speed of the mail train is 12 km/hr more than that of an express train.
II.      A mail train takes 40 minutes less than an express train to cover the distance.

A.     I alone sufficient while II alone not sufficient to answer
B.     II alone sufficient while I alone not sufficient to answer
C.     Either I or II alone sufficient to answer
D.     Both I and II are not sufficient to answer
E.     Both I and II are necessary to answer
Explanation:
Let the distance between the two stations be x km.
I. Then, speed of the mail train = (y + 12) km/hr.
II.  x      -        x         = 40 .
y         (y + 12)        60
Thus, even I and II together do not give x.
Correct answer is (D).

17. If Rs. 782 be divided into three parts, proportional to 1/2: 2/3: 3/4,  then the first part is:
A. Rs. 182
B. Rs. 190
C. Rs. 196
D. Rs. 204
Explanation
: Given ratio = 1/2: 2/3: 3/4  = 6 : 8 : 9
1st part = Rs.(782 x 6/23) = Rs.204

18.   The fourth proportional to 5, 8, 15 is:
A.     18
B.     24
C.     19
D.     20
Explanation:
Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
=>  5x = (8 x 15)
x = (8 x 15) = 24.
5

19.     A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
A.     11:30 A.M.
B.     12 noon
C.     12:30 P.M.
D.     1:00 P.M.
Explanation
: (P + Q + R)'s  1 hour's work  = ( 1/8+ 1/10 + 1/12 ) = 37/120.
Work done by P, Q and R in 2 hours = ( (37/120)  x 2 ) = 37/60
Remaining work = ( 1 - 37 ) =         23
60               60

(Q + R)'s 1 hour's work = ( 1/10 + 1/12 ) = 11 /60
Now,  11 work is done by Q and R in 1 hour.
60

So, 23 work will be done by Q and R in ( 60/11 x 23/60 ) = 2311  hours = 2 hours.
60
So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

20. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
A.     9  1 days
5

B.     9  2 days
5

C.     9  3 days
5
D.     10

Explanation:
(A + B + C)'s 1 day's work = 1/4 ,
A's 1 day's work =  1 ,
16
B's 1 day's work =  1 .
12

Therefore C's 1 day's work =  1  -     ( 1   +    1 ) = ( 1 -   7 ) =   5
4          16      12       4    48       48

So, C alone can do the work in  48 = 9 3 days.
5          5

21.     The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
A.     1677
B.     1683
C.     2523
D.     3363
Explanation:
L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840 k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
:. Required number = (840 x 2 + 3) = 1683.

22. If      144         = 14.4 , then the value of x is:
0.144             x
A.     0.0144
B.     1.44
C.     14.4
D.     144
Explanation
:        144      = 14.4
0.144         x
=>  144 x 1000 =     14.4
144                   x
=> x =  14.4    = 0.0144
1000

23.    3. 617 + 6.017 + 0.617 + 6.0017 = ?
A.     6.2963
B.     62.965
C.     629.6357
D.     None of these
Explanation:
617.00
6.017
0.617
+ 6.0017
-------------
629.6357
---------------

24.    (√3 - (1√3))2 simplifies to :
A.    3/4
B.    4/√3
C.    4/3
D.    None of these
Answer : Option C
Explanation :
(√3 - (1/√3))2 = (√3)2 +  (1/√3)2 - 2 x √3 x 1/√3
= 3 + (1/3)-2
= 1+ 1/3
= 4/3

25.     A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
A.     65 sec
B.     89 sec
C.     100 sec
D.     150 sec
Explanation:
Speed = 240 m/sec = 10 m/sec.
24
Required time =( (240 + 650)/ 10) sec = 89 sec.

26.    A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?
A.     2 p.m. on Tuesday
B.     2 p.m. on Wednesday
C.     3 p.m. on Thursday
D.     1 p.m. on Friday
Explanation
:    Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.
:. The watch gains (2 + 4 and 4/5 min. or 34/5 min. in 170 hrs.
Now, 34/5 min. are gained in 170 hrs.
:. 2 min. are gained in (170 x 5/34 x 2) hrs = 50 hrs.
Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday.

27.    The banker's discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is:
A.     3 months
B.     4 months
C.     6 months
D.     8 months
Explanation:
S.I. on Rs.1600 = T.D. on Rs.1680.
:. Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
:.  Time = (100 x 80)/1600 x 15 year = 1/3 year = 4 months.

28.    In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A.     30%
B.     70%
C.     100%
D.     250%
Explanation:
Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage = (295/420 x 100 % =    1475 % = 70% (approximately).
21

29.    In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
A.     360
B.     480
C.     720
D.     5040
E.     None of these
Explanation
: The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.

30.    Present ages of Seema and Naresh are in the respective ratio of 5:7. Five years hence the ratio  of their ages becomes 3:4 respectively. What is Naresh's present age in years ?
A.    25
B.    40
C.    30
D.    Cannot be determined
E.    None of these
Answer : Option E
Explanation :
Let the present ages of Seema and Naresh be 5x and 7x years respectively
According to the question,
5x+5    =   3
7x+5         4

=> 21x + 15 = 20 x + 20
=> x = 20-15 = 5
:. Naresh's present age
=7x years
= 7 x 5 = 35 years