Simplification I

Q1
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 ?
Ans:

      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.

Q2

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?

Ans:

      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.

Q3

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?

Ans:

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

      Then, 10x = 4y   or   y =5x/2.

       15x + 2y = 4000

       15x + 2 x 5x/2=4000

       20x = 4000

       x = 200.

      So, y = 5 x 200 / 2 = 500.

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

      = Rs. (2400 + 1500)

      = Rs. 3900.

Q4

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

Ans:

      (a - b)2 = a2 -2ab + b2 

      2ab = (a2 + b2) - (a - b)2

      = 29 - 9 = 20

      ab = 10.

Q5

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 ?

Ans:

      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

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4y = 800

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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.