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