Question

Three numbers A, B and C are in the ratio 1 : 2 : 3 Their average is 600 If A is increased by 10% and B is decreased by 20%, then by how much will C be increased to get the average increased by 5% ?

Answer 1

Let $A=x,B=2x$ and $C=3x$
Given $\frac{x+2x+3x}{3}=600\Rightarrow 6x=1800\Rightarrow x=300$
$\therefore$ The numbers are $A=300,B=600,C=900$
New average 105% of 600 $=\frac{105}{100}\times 600=630$
New value of $A=\frac{110}{100}\times 300=330$
New value of $B=\frac{80}{100}\times 600=480$
Let new value of $C=y$

Then $\frac{330+480+y}{3}=630$

$\Rightarrow 810+y=1890$
$\Rightarrow y=1080$

$\therefore$ Increase in $C=\frac{(1080-900)}{900}\times 100=20\%$