Question

Rs 6504 are to be shared among three persons so that first person gets 90% of the second who in turn gets 90% of the third. How much amount will each of them get?

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Answer 1

$\sf \Large Solution!!$

$\sf \large Given:$

$\sf \to Total\:amount=Rs.\:6,504$

$\sf \to Share\:of\:1st\:person=90\%\:of\:2nd\:person$

$\sf \to Share\:of\:2nd\:person=90\%\:of\:3rd\:person$

$\sf \large To\:find:$

$\sf \to Amount\:received\:by\:each\:person.$

$\sf \large Let,$

$\sf \to Share\:of\:3rd\:person=x$

$\sf \large Now,$

$\sf \to Share\:of\:2nd\:person=90\%\:of\:x$

$\sf \to Share\:of\:2nd\:person=\dfrac{9\cancel{0}}{10\cancel{0}}\times x$

$\sf \to Share\:of\:2nd\:person=0.9x$

$\sf \large Similarly,$

$\sf \to Share\:of\:1st\:person=90\%\:of\:0.9x$

$\sf \to Share\:of\:1st\:person=\dfrac{90}{100}\times 0.9x$

$\sf \to Share\:of\:1st\:person=\dfrac{81x}{100}$

$\sf \to Share\:of\:1st\:person=0.81x$

$\sf \large So,$

$\sf \to Share\:of\:1st\:person+Share\:of\:2nd\:person+Share\:of\:3rd\:person=Rs.\:6,504$

$\sf \to 0.81x+0.9x+x=Rs.\:6,504$

$\sf \to 2.71x=Rs.\:6,504$

$\sf \to x=\dfrac{\cancel{6,504}\;\;^{2,400}}{\cancel{2.71}}$

$\sf \to x=Rs.\:2,400$

$\sf \large Now,$

$\sf \to Share\:of\:1st\:person=0.81x$

$\sf \to Share\:of\:1st\:person=0.81\times Rs.\:2,400$

$\sf \boxed{\bigstar Share\:of\:1st\:person=Rs.\:1,944}$

$\sf \to Share\:of\:2nd\:person=0.9x$

$\sf \to Share\:of\:2nd\:person=0.9\times Rs.\:2,400$

$\sf \boxed{\bigstar Share\:of\:2nd\:person=Rs.\:2,160}$

$\sf \to Share\:of\:3rd\: person=x$

$\sf \boxed{\bigstar Share\:of\:3rd\:person=Rs.\:2,400}$

$\sf \large Verification:$

$\sf \to Rs.\:1,944+Rs.\:2,160+Rs.\:2,400=Rs.\:6,504$

$\sf \to Rs.\:6,504=Rs.\:6,504$

$\sf L.H.S=R.H.S$

$\sf Hence,\: verified.$

Thanks for asking!! :)