Tag: vedic mathematics

$(112\times {5}^{4})=112\times { \left( \cfrac { 10 }{ 2 }  \right)  }^{ 4 }=\cfrac { 112\times { 10 }^{ 4 } }{ { 2 }^{ 4 } } =\cfrac { 1120000 }{ 16 } =70000$

Required numbers are $10,15,20,25,......96$
This is an A.P. in which $a=10,d=5$ and $l=95$
${t} _{n}=95$ $\Rightarrow$ $a+(n-1)d=95$
$\Rightarrow$ $10+(n-1)\times 5=95$
$\Rightarrow$ $(n-1)\times 5=85$
$\Rightarrow$ $(n-1)=17$
$\Rightarrow$ $n=18$
$\therefore$ Required Sum $=\cfrac { n }{ 2 } (a+l)=\cfrac { 18 }{ 2 } \times (10+95)=(95\times 105)=945$

$5358\times 51=5358\times (50+1)$
$=5358\times 50+5358\times 1$
$=267900+5358$
$=273258$

1397×1397=13972.