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The present age of father is thrice that of his son's age.Five years from now father's age will be 8 years more than twice of his son's age. Find their present age |
| Answer» <html><body><p> <img align="absmiddle" alt="\huge\boxed{\fcolorbox{red}{ink}{Consider:}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%5Cfcolorbox%7Bred%7D%7Bink%7D%7BConsider%3A%7D%7D" title="\huge\boxed{\fcolorbox{red}{ink}{Consider:}}"/></p><ul><li>Let the present <a href="https://interviewquestions.tuteehub.com/tag/age-851457" style="font-weight:bold;" target="_blank" title="Click to know more about AGE">AGE</a> of the father be a and the present age of the son be b </li></ul><p></p><p><img align="absmiddle" alt="\huge\boxed{\fcolorbox{purple}{ink}{GIVEN:}}" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%5Cfcolorbox%7Bpurple%7D%7Bink%7D%7BGIVEN%3A%7D%7D" title="\huge\boxed{\fcolorbox{purple}{ink}{GIVEN:}}"/></p><p>It is given that The present age of father is thrice that of his son's age.</p><p></p><p><img align="absmiddle" alt="x−5=3(y−5) \\ \\x−5=3y−15 \\ \\ x−3y=−15+5 \\ \\x−3y=−10 \: \: \: \: \: (1)" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=x%E2%88%925%3D3%28y%E2%88%925%29%20%5C%5C%20%20%5C%5Cx%E2%88%925%3D3y%E2%88%9215%20%5C%5C%20%20%5C%5C%20x%E2%88%923y%3D%E2%88%9215%2B5%20%5C%5C%20%20%5C%5Cx%E2%88%923y%3D%E2%88%9210%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%281%29%20" title="x−5=3(y−5) \\ \\x−5=3y−15 \\ \\ x−3y=−15+5 \\ \\x−3y=−10 \: \: \: \: \: (1)"/></p><p></p><p><img align="absmiddle" alt="\huge\fbox\pink{✯Condition✯}" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%5Chuge%5Cfbox%5Cpink%7B%E2%9C%AFCondition%E2%9C%AF%7D" title="\huge\fbox\pink{✯Condition✯}"/></p><ul><li>Five years from now father's age will be 8 years more than twice of his son's age.</li></ul><p></p><p><img align="absmiddle" alt="x+5=2(y+8) \\ \\x+8=2y+16 \\ \\ x−2y=16-5 \\ \\x−2y= 11 \: \: \: \: \: (2)" class="latex-formula" id="TexFormula5" src="https://tex.z-dn.net/?f=x%2B5%3D2%28y%2B8%29%20%5C%5C%20%20%5C%5Cx%2B8%3D2y%2B16%20%5C%5C%20%5C%5C%20x%E2%88%922y%3D16-5%20%5C%5C%20%20%5C%5Cx%E2%88%922y%3D%2011%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%282%29" title="x+5=2(y+8) \\ \\x+8=2y+16 \\ \\ x−2y=16-5 \\ \\x−2y= 11 \: \: \: \: \: (2)"/></p><p><img align="absmiddle" alt="\huge\boxed{\dag\sf\red{NOW}\dag}" class="latex-formula" id="TexFormula6" src="https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%5Cdag%5Csf%5Cred%7BNOW%7D%5Cdag%7D" title="\huge\boxed{\dag\sf\red{NOW}\dag}"/></p><ul><li>Subtract <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> 1 from equation 2 to eliminate x as the <a href="https://interviewquestions.tuteehub.com/tag/coefficients-920961" style="font-weight:bold;" target="_blank" title="Click to know more about COEFFICIENTS">COEFFICIENTS</a> of x are same </li></ul><p></p><p></p><ul><li>(x−x)+(−2y+3y)=5+11</li></ul><p></p><p>i.e. y=16</p><p></p><ul><li>place this <a href="https://interviewquestions.tuteehub.com/tag/value-1442530" style="font-weight:bold;" target="_blank" title="Click to know more about VALUE">VALUE</a> of y in (2), we get</li></ul><p></p><p>x−32=11</p><p></p><p>i.e. x=11+32=<a href="https://interviewquestions.tuteehub.com/tag/43-316498" style="font-weight:bold;" target="_blank" title="Click to know more about 43">43</a></p><p></p><p></p><p><img align="absmiddle" alt="\huge\boxed{\dag\sf\red{Therefore}\dag}" class="latex-formula" id="TexFormula7" src="https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%5Cdag%5Csf%5Cred%7BTherefore%7D%5Cdag%7D" title="\huge\boxed{\dag\sf\red{Therefore}\dag}"/></p><p></p><p></p><p>The present age of the father is 43 years and the present age of the son is 16 years.</p></body></html> | |