| Sum of square of first number and cube of second number is 568 together. Also square of the second number is 15 less than square of 8. What is the value of three-fifth of the first number? (Assuming both the numbers are positive) |
A) 18
B) 8
C) 9
D) 16
E) None of these
Correct Answer: C
Solution :
| Suppose first number \[=x\] |
| and second number \[=y\] |
| Then, \[{{8}^{2}}-{{y}^{2}}=15\] |
| \[\Rightarrow \] \[{{y}^{2}}=64-15=49\] |
| \[\Rightarrow \] \[y=7\] |
| Also, \[{{x}^{2}}+{{y}^{3}}=568\] |
| \[\Rightarrow \] \[{{x}^{2}}+{{7}^{3}}=568\] |
| \[\Rightarrow \] \[{{x}^{2}}=568-343\] |
| \[\Rightarrow \]\[{{x}^{2}}=225\]\[\Rightarrow \]\[x=15\] |
| Hence, \[\frac{3}{5}\times \]first number \[=\frac{3}{5}\times 15=9\] |
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