Quiz- 1

x3+y3 = (x + y) × (x2 − xy + y2)



Putting given values of x3+y3 and (x + y)

9 = 3 × ((x+y)2 − 3xy)

  = 3 × (9 − 3xy) 

  = 27 − 9xy



9xy = 18

xy = 2



x4 + y4 = (x2 + y2)2 - 2x2y2

   = (x2 + y2)2 - 2*4 

                                  [Putting value of xy]

   = ((x + y)2 - 2xy)2 - 2*4 

                            [Putting values of (x+y) and xy]

   = (9 - 4)2 - 2*4 

   = 17

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

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.

Explanation:

Explanation:

Let the total number of shots be x. Then,

Shots fired by A =	5	x
	8

Shots fired by B =	3	x
	8

Killing shots by A =	1	of	5	x	=	5	x
	3		8			24

Shots missed by B =	1	of	3	x	=	3	x
	2		8			16

	3x	= 27 or x =		27 x 16		= 144.
	16			3

Birds killed by A =

5x

=

5

x 144

= 30.

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.

Explanation:

Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,

1	x =	1	(150000 - x)
3		2

	x	+	x	= 75000
	3		2

	5x	= 75000
	6

x =	75000 x 6	= 90000
	5

Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000

Explanation:

[5-(11)+4]+2

5-11+4+2

0

Explanation :

9(-4x+10)+7x=0

90=(36-7)x

x=90/29