Simplification

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: B

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.

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

A:

10

B:

12

C:

15

D:

18

Answer: A

2ab = (a² + b²) - (a - b)²

= 29 - 9 = 20

ab = 10.

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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: D

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.

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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: 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.

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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: 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.

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Questions for: Simplification