Question

The density of metal A' is 5.6 units 12 kg of metal A' is mixed with 9 kg of metal to form an alloy. If the density of the alloy is 6.5 units, what is the density of metal B
1) 81 units
2) 7.7 units
3) 7.5 units
4) 73 units
5) None of these​

Answer 1

Given density of metal A = 5.6 units

mass of A = 12 kg

density of A = mass of A/volume of A

volume of A = 12/5.6 = 15/7

mass of B = 9 kg

Let volume of B = V

mass of alloy = mass of A + mass of B = 21 kg

volume of alloy = volume of A + volume of B = (15/7 + V)

density of alloy = mass of alloy/volume of alloy

6.5 = 21/(15/7 + V)

13/2 = 21/(15/7 + V)

195/14 + 13V/2 = 21

13V/2 = 21 - 195/14

13V/2 = 99/14

V = 99/91

Density of B = mass of B/volume of B

= 9/(99/91)

= 8.27 nearly

So, none of the options are correct.