question_answer

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 to get the average increased by 5%. C will be increased by               [NICL (AO) 2014]

 

A) 90%                             

B) 10%

C) 15%                             

D) 18%

E) 20%

Correct Answer: E

Solution :

Let A = x, B = 2x and C = 3x

Then, \[\frac{x+2x+3x}{3}=600\]\[\Rightarrow \]\[\frac{6x}{3}=600\]

\[\frac{x}{3}=100\]\[\Rightarrow \]\[x=300\]

\[\therefore \] Numbers are 300, 600 and 900.

New average = 105% of \[600=\frac{600\times 105}{100}=630\]

Now, let

\[\Rightarrow \]   \[300\times \frac{110}{100}+600\times \frac{80}{100}+y=1890\]

\[\Rightarrow \]   \[330+480+y=1890\]

\[\Rightarrow \]               \[810+y=1890\]

\[\Rightarrow \]   \[y=1890-810=1080\]

\[\therefore \] Increase in \[C=1080-900=180\]

% increase in \[C=\frac{180}{900}\times 100=20%\]