BdMO National Primary 2015#2

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samiul_samin
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BdMO National Primary 2015#2

Unread post by samiul_samin » Tue Feb 19, 2019 10:26 am

Four people $A, B, C$ and $D$ have an average monthly income of $10000$ taka. First three of them have an average monthly income of $12000$ taka. Average income of first two of them is $15000$ taka. Find the monthly income of $B, C$ and $D$ if $A$ has a monthly income of $20000$ taka?

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samiul_samin
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Re: BdMO National Primary 2015#2

Unread post by samiul_samin » Sat Feb 23, 2019 1:12 pm

Let $a,b,c,d$ denote their respective incomes.Then the given conditions are:

$\dfrac {a+b+c+d}{4}=10000\Rightarrow a+b+c+d=40000...(i)$

$\dfrac {a+b+c}{3}=12000\Rightarrow a+b+c+d=36000...(ii)$

$\dfrac {a+b}{2}=15000\Rightarrow a+b+c+d=30000...(iii)$

$a=20000...(iv)$

$(iii)$ & $(iv)$ $\Rightarrow b=10000$

$(ii)$ & $(iii)$ $\Rightarrow c=6000$

$(i)$ & $(ii)$ $\Rightarrow d=4000$

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