| If the sum of two numbers, one of which is \[\frac{2}{5}\] times the other is 50, then the numbers are |
A) \[\frac{240}{7},\]\[\frac{110}{7}\]
B) \[\frac{250}{7},\]\[\frac{100}{7}\]
C) \[\frac{115}{7},\]\[\frac{236}{7}\]
D) \[\frac{150}{7},\]\[\frac{200}{7}\]
Correct Answer: B
Solution :
| Let the first number be x. |
| Then, other number be \[\frac{2}{5}x.\] |
| According to the question, |
| \[x+\frac{2}{5}x=50\]\[\Rightarrow \]\[\frac{7x}{5}=50\]\[\Rightarrow \]\[x=\frac{250}{7}\] |
| Other number \[=\frac{2}{5}\times \frac{250}{7}=\frac{100}{7}\] |
| \[\therefore \]The numbers are \[\left( \frac{250}{7},\frac{100}{7} \right).\] |
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