Simplification

Question:
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

Answer: Option D

Explanation:

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:
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

Answer: Option C

Explanation:

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: The price of 2 sarees and 4 shirts is Rs. 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].

Rs. 1200

[B].

Rs. 2400

[C].

Rs. 4800

[D].

Cannot be determined

Answer: Option B

Explanation:

Let the price of a saree and a shirt be Rs. x and Rs. 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 = Rs. (12 x 200) = Rs. 2400.

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

[A].

Rs. 3500

[B].

Rs. 3750

[C].

Rs. 3840

[D].

Rs. 3900

Answer: Option D

Explanation:

Let the cost of a chair and that of a table be Rs. 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

    = Rs. (2400 + 1500)

    = Rs. 3900.

Question:
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:

[A].

1

7

[B].

1

8

[C].

1

9

[D].

7

8

Answer: Option A

Explanation:

Original share of 1 person =	1
	8

New share of 1 person =	1
	7

Increase =		1	–	1		=	1
		7		8			56

Required fraction =	(1/56)	=		1	x	8		=	1
	(1/8)			56		1			7

Question: A man has Rs.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

Answer: Option D

Explanation:

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

[A].

160

[B].

175

[C].

180

[D].

195

Answer: Option B

Explanation:

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:
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

Answer: Option C

Explanation:

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:
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

Answer: Option C

Explanation:

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:
If a – b = 3 and a2 + b2 = 29, find the value of ab.

[A].

10

[B].

12

[C].

15

[D].

18

Answer: Option A

Explanation:

2ab = (a2 + b2) – (a – b)2

   = 29 – 9 = 20

   ab = 10.