A) 19
B) 20
C) 21
D) 23
Correct Answer: A
Solution :
| Let two numbers be x and 7 respectively. |
| According to the given condition, |
| \[x\times (x+y)=247\] ...(i) |
| and \[y\times (x+y)=114\] ...(ii) |
| On the dividing Eq. (i) by Eq. (ii) we get |
| \[\frac{x}{y}=\frac{247}{114}=\frac{13}{6}\] |
| \[\Rightarrow \] \[x=\frac{13}{6}y\] ?(iii) |
| Put the value of x from Eq. (iii), in Eq. (i), we get |
| \[\frac{13}{6}y\times \left( \frac{13}{6}y+y \right)=247\] |
| \[\Rightarrow \] \[\frac{13}{6}y\times \frac{19}{6}y=247\] |
| \[\Rightarrow \] \[{{y}^{2}}=\frac{6\times 6\times 247}{13\times 19}\] |
| \[\Rightarrow \] \[{{y}^{2}}=36\]\[\Rightarrow \]\[y=\sqrt{36}=6\] |
| Now, put the value of y in Eq. (iii), we get |
| \[x=\frac{13}{6}\times 6\]\[\Rightarrow \]\[x=13\] |
| \[\therefore \]The sum of two numbers\[=x+y=13+6=19\] |
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