Math, asked by srujanaankam8194, 10 months ago

ഒരാളുടെ കൈയിൽ 100 രൂപ ഉണ്ട്. അയാൾക്ക് ഈ രൂപ കൊണ്ട് പ്ലേറ്റും,ഗ്ലാസ്സും,സ്പൂണും വാങ്ങണം.

Answers

Answered by Swarup1998
1

Given:

  • Cost of a plate = Rs. 5
  • Cost of a glass = Rs. 3
  • Cost of 40 spoons = Rs. 1
  • ⇒ Cost of a spoon = Rs. 1/40

Consideration:

  • Number of plates = x
  • Number of glasses = y
  • Number of spoons = z

Now we proceed towards the solution:

For total quantity 100, x + y + z = 100

For total cost Rs. 100, 5x + 3y + z/40 = 100

We cannot solve the two equations with three variables in any direct method.

That is why, we take z = 0, 40, 80 (< 100) to get integral values of x and y.

Here z = 0 cannot be taken as spoons must be bought.

For z = 40:

We have new set of equations,

  • x + y = 60
  • 5x + 3y = 99

Multiplying the 1st equation by 5, we get

5x + 5y = 300

Subtracting the second equation from it, we get

2y = 201

or, y > 201/2, which is not an integral value.

So z ≠ 40.

For z = 80

We have new set of equations:

  • x + y = 20 ..... (i)
  • 5x + 3y = 98 ..... (ii)

(i) × 5 gives

5x + 5y = 100 ..... (iii)

(iii) - (ii) gives

2y = 2

or, y = 1

Then x = 19.

Thus z = 80 can be an appropriate value.

Answer:

  • Number of plates = 19
  • Number of glasses = 1
  • Number of spoons = 80

Confirmation:

So total items = 19 + 1 + 80 = 100

& total cost = Rs. (19 × 5) + (1 × 3) + (80/40)

= Rs. (95 + 3 + 2)

= Rs. 100

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