Simplification - General Questions (2)

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

	x	+	x	= 75000
	3		2

	5x	= 75000
	6

x =	75000 x 6	= 90000
	5

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

Let C's share = Rs. x

Then, B's share = Rs.	x	,   A's share = Rs.		2	x	x		= Rs.	x
	4			3		4			6

	x	+	x	+ x = 1360
	6		4

	17x	= 1360
	12

x =	1360 x 12	= Rs. 960
	17

Hence, B's share = Rs.		960		= Rs. 240.
		4

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.

2ab = (a² + b²) - (a - b)²

   = 29 - 9 = 20

   ab = 10.

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

 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.

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.

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.