Question

A nugget of gold and quartz was found to contain x g of gold and y g of quartz and has density d. If the densities of gold and quartz are d1 and d2 respectively then the correct relation is :

(A) d1 x + d2 y =x+y/d
(B) xd1 + yd2 = (x + y)d
(C) d2 x + d1 y = x+y/d
(D) x+y/d + x/d1 + y/d2 = 0

Answer 1

Density d = Mass ÷ Volume

Here we have,

d =(mass of gold + mass of quartz) ÷ (volume occupied by gold + quartz)

volume of gold = x/d1

Similarly volume of quartz = y/d2

So we have,

d = (x + y) ÷ ( x/d1 + y/d2)

Multiply and divide the denominator above by d1.d2, we get

d = (x + y) ÷ (d2.x + d1.y)

Or we can write,

(d2.x + d1.y) ÷ (x + y) = 1/d

d2.x + d1.y = (x + y) ÷ d

i.e. our option C