Question

27. in an election between four candidates a, b, c and d, a gets 20% votes more than b, c gets 10% votes less than b, and d gets 15% votes more than a. If a gets 120000 votes, then how many votes are polled in the election?(a) 484000 (b) 448000(c) 420000 (d) 450000

Answer 1

$A,B,C \:and\:D \:are \: 4 \: contestants \: in \\an \: election$

$Let \: Number \: of \: votes \: B \:get = x$

$Number \: of \: votes \: A \:get= 120000 \: votes\: ---(1)$

$\implies 20\% \: more \: than \: B=120000$

$\implies x\Big( \frac{100+20}{100} \Big)= 120000$

$\implies \frac{120x}{100} =120000$

$\implies x = 120000 \times \frac{100}{120}$

$\implies x = 100000$

$Number \: of \: votes \: B \:get (x) = 100000\: --(2)$

$Number \: of \: votes \: C \:get (x)\\ = 10\%\: less \:than \: B \\= 100000\Big( \frac{100-10}{100}\Big) \\= 100000\times \frac{90}{100} \\= 90000\: ---(3)$

$Number \: of \: votes \: D\:get (x)\\ = 15\%\: more \:than \: A \\= 100000\Big( \frac{100+15}{100}\Big) \\= 100000\times \frac{115}{100} \\= 138000\: ---(4)$

$\red { Total \:votes \: polled } \\= (1)+(2)+(3)+(4) \\= 120000 + 100000 + 90000 + 138000 \\= 448000$

Therefore.,

$Option \: \pink { (b) } \: is \: correct .$

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