Question

1. निम्नलिखित संख्याओं का HCF ज्ञात करने के लिए यूक्लिड विभाजन एल्गोरिथ्य का प्रयोग कीजिए :
(i) 135 और 225
(ii) 196 और 38220
(iii) 867 और 255
(iv) 37728 और 12156​

Answer 1

Answer:

$</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\begin{lgathered}\Huge\bigstar\:\tt\underline\red{GIVEN}\\\\\\\end{lgathered}★GIVEN</p><p></p><p>\begin{lgathered}\bullet\:\:\:\:\sf\orange{ Akhil \:is\: twice\: as\: old\: as \:Bharath}\\\end{lgathered}∙AkhilistwiceasoldasBharath</p><p></p><p>\bullet\:\:\:\:\sf \orange{Ten\: years\: ago, \;Akhil's\: age\: was \:four\: times\: Bharath's \:age.}∙Tenyearsago,Akhil′sagewasfourtimesBharath′sage.</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p></p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\begin{lgathered}\Huge\bigstar\:\tt\underline\red{TO\:FIND}\\\\\\\end{lgathered}★TOFIND</p><p></p><p>\bullet\:\:\:\:\sf\orange{{\Large The \:present \:age \:of \:Akhil} }∙ThepresentageofAkhil</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p></p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\begin{lgathered}\Huge\bigstar\:\tt\underline\red{SOLUTION}\\\\\\\end{lgathered}★SOLUTION</p><p></p><p>\sf\underline\pink{Let }Let</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\sf\orange{{\large Present \:age \:of\: Bharath \:be\: x}}PresentageofBharathbex</p><p></p><p>\sf\orange{{\Large Akhil \:age \:be \:2x}}Akhilagebe2x</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\sf\underline\pink{After \:10 \:years\: ago }After10yearsago</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\sf\orange{{\Large Bharath's\: age\: =\: (x - 10)}}Bharath′sage=(x−10)</p><p></p><p>\sf\orange{{\Large Akhil's \:age \:=\: (2x - 10)}}Akhil′sage=(2x−10)</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\Large\leadsto\:\:\: \: \sf \purple {2x - 10 = 4(x - 10)}⇝2x−10=4(x−10)</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\Large\leadsto\:\:\: \: \sf \green {2x - 10 = 4x - 40 }⇝2x−10=4x−40</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\Large\leadsto\:\:\: \: \sf \purple {40 - 10 = 4x - 2x }⇝40−10=4x−2x</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\Large\leadsto\:\:\: \: \sf \green {2x = 30}⇝2x=30</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\Large\leadsto\:\:\: \: \sf \purple {x = {\huge\frac{30}{2}} }⇝x=230</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\Large\leadsto\:\:\: \: \sf \green {x = 15}⇝x=15</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\sf\orange{Hence, }Hence,</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\large\dagger\:\sf\underline\pink{Present\: age \:of \:Bharath}\: :†PresentageofBharath:</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\Large\leadsto\:\:\: \: \sf \purple {x = 15\:years }⇝x=15years</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\large\dagger\:\sf\underline\pink{Present \:age \:of \:Akhil} \: :†PresentageofAkhil:</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\Large\leadsto\:\:\: \: \sf \green {2x = 2 × 15 }⇝2x=2×15</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p>\Large\leadsto\:\:\: \: \sf \underline\green {30\:years}⇝30years</p><p></p><p>\begin{lgathered}\\\end{lgathered}</p><p></p><p></p><p></p><p>$