Question 1
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

A
20
B
80
C
100
D
200
Correct Answer: Option C

Let the number of students in rooms A and B be x and y respectively.

Then, x - 10 = y + 10      x - y = 20 .... (i)

     and x + 20 = 2(y - 20)      x - 2y = -60 .... (ii)

Solving (i) and (ii) we get: x = 100 , y = 80.

The required answer A = 100.

Question 2
The price of 2 sarees and 4 shirts is ₹ 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?

A
₹ 1200
B
₹ 2400
C
₹ 4800
D
Cannot be determined
E
None of these
Correct Answer: Option

Let the price of a saree and a shirt be ₹x and ₹ y respectively.

Then, 2x + 4y = 1600 .... (i)

    and x + 6y = 1600 .... (ii)

Divide equation (i) by 2, we get the below equation.

=> x + 2y = 800. --- (iii)

Now subtract (iii) from (ii)

 x +  6y = 1600 (-)
 x +  2y =  800  
----------------
      4y =  800
----------------

Therefore, y = 200.

Now apply value of y in (iii)

=> x + 2 x 200 = 800

=> x + 400 = 800

Therefore x = 400

Solving (i) and (ii) we get x = 400, y = 200.

Cost of 12 shirts = ₹ (12 x 200) = ₹ 2400.

Question 3
A man has ₹ 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

A
45
B
60
C
75
D
90
Correct Answer: Option D

Let number of notes of each denomination be x.

Then x + 5x + 10x = 480

16x = 480

x = 30.

Hence, total number of notes = 3x = 90.

Question 4
If a - b = 3 and a2 + b2 = 29, find the value of ab.

A
10
B
12
C
15
D
18
Correct Answer: Option A

2ab = (a2 + b2) - (a - b)2

   = 29 - 9 = 20

   ab = 10.

Question 5
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is ₹ 4000. The total price of 12 chairs and 3 tables is:

A
₹ 3500
B
₹ 3750
C
₹ 3840
D
₹ 3900
Correct Answer: Option D

Let the cost of a chair and that of a table be ₹ x and Rs. y respectively.

Then, 10x = 4y   or   y = 5 x.
2

15x + 2y = 4000

15x + 2 x 5 x = 4000
2

20x = 4000

x = 200.

So, y = 5 x 200 = 500.
2

Hence, the cost of 12 chairs and 3 tables = 12x + 3y

    = ₹ (2400 + 1500)

    =₹ 3900.

Question 6
David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

A
19
B
28
C
30
D
37
Correct Answer: Option C

Suppose their paths cross after x minutes.

Then, 11 + 57x = 51 - 63x      120x = 40

x = 1
3

Number of floors covered by David in (1/3) min.

= 1 x 57 = 19.
3

So, their paths cross at (11 +19) i.e., 30th floor.

Question 7
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets ₹ 2.40 per hour for regular work and ₹ 3.20 per hours for overtime. If he earns ₹ 432 in 4 weeks, then how many hours does he work for ?

A
160
B
175
C
180
D
195
Correct Answer: Option B

Suppose the man works overtime for x hours.

Now, working hours in 4 weeks = (5 x 8 x 4) = 160.

160 x 2.40 + x x 3.20 = 432

3.20x = 432 - 384 = 48

x = 15.

Hence, total hours of work = (160 + 15) = 175.

Question 8
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:

A
22
B
23
C
24
D
26
Correct Answer: Option D

Let the number of hens be x and the number of cows be y.

Then, x + y = 48 .... (i)

  and 2x + 4y = 140      x + 2y = 70 .... (ii)

Solving (i) and (ii) we get: x = 26, y = 22.

The required answer = 26.

Question 9
Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?

A
256
B
432
C
512
D
640
E
None of these
Correct Answer: Option C

Let total number of children be x.

Then, x x 1 x = x x 16    x = 64.
8 2

Number of notebooks :

= 1 x2 = 1 x 64 x 64 = 512.
8 8

Question 10

(469 + 174)2 - (469 - 174)2 = ?
(469 x 174)

A
2
B
4
C
295
D
643
Correct Answer: Option B

Given exp. = (a + b)2 - (a - b)2
ab

   = 4ab
ab

   = 4 (where a = 469, b = 174.)

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