Question

R's 6504 are to be shared among three person so that first person get 90% of the second who in turn get 90% of rhe third. how much amount will each of them get ​

Answer 1

Let the share of the third person be x.

Second person has 90% of x

$\sf \implies \: \frac{90}{100} x \\ \sf \: = \frac{9}{10} x$

$\sf \: First \: person \: has \: 90\% \: of \: \frac{9}{10} x \\ \sf \: = \frac{90}{100} \times \frac{9}{10}x \\ \sf \: = \: \frac{81}{100} x$

$\sf \therefore \: x + \frac{9}{10} x + \frac{81}{100} x = 6504\\ \\ \sf \: \frac{1000x + 900x + 810x}{1000} = 6504 \\ \\ \sf \: \frac{2710x}{1000} = 6504 \\ \\ \sf \: x = \frac{ \cancel{6504} \: ^{24} \times 100 \cancel0}{ \cancel{271} \cancel0} \\ \\ \sf \: x = 2400$

$\sf \: Now,$

$\sf \: Third \: person = x \\ \boxed{ \red{ \sf= Rs. 2400}}$

$\sf \: Second \: person = \frac{9}{10} x \\ \sf = \frac{9}{1 \cancel0} \times 240 \cancel0 \\ \boxed{ \red {\sf{ = Rs.2160}}}$

$\sf \:First \: person = \frac{81}{100} x \\ \sf \: = \: \frac{81}{1 \cancel{00}} \times 24 \cancel{00 }\\ \boxed{ \red{\sf \: = \: Rs. \: 1944}}$