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