Question

A toy weighing 24 grams of an alloy of two metals is worth Rs 174/-, but if the weights of the two metals be interchanged, the toy would be worth Rs 162/- If the price of one metal be Rs 8 per ,gram, find the price of the other metal used to make the toy

Answer 1

The weight of the toy is 24 g

If  the weight of one of the metal is x, then the weight of the other will be 24-x

Let us assume that the price of one is y rupees - the other is 8 rupees (given)...That means the price of metal is its price times its weight.

Therefore;

y ( x) + 8(24-x) = 172

xy + 192 - 8x = 174


When you interchange the weight:

8(x) + y(24-x) = 162

8x + 24y -xy = 162

Add the two equations to find the value of y:


8x + 24y - xy = 162 
                                  +
xy + 192 - 8x = 174

24y + 192 = 336

24y = 336 -192

24y = 144

y = 6
The price of the other metal is 6 rupees per gram

Use the value of y to find the value of x

xy + 192 - 8x = 174
6x + 192 - 8x = 174

6x-8x = 174-192

-2x = -18

x = -18/-2

x= 9



Therefore one the metals weigh 9g

If 1 is 9 g the other is 24g -9g =15g


The price of the of the other metal is 6 rupees per gram