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# A sum of 2236 is divided among A, B and C such that A receives $25%$ more than C and C receives $25%$ less than B. What is A’s share in amount?\begin{align} & \left( A \right)Rs.460 \\ & \left( B \right)Rs.890 \\ & \left( C \right)Rs.780 \\ & \left( D \right)Rs.1280 \\ \end{align}

Last updated date: 24th Jul 2024
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Hint: To solve this problem, we will first take three variables and write an equation on them. After this, we are given the relationship between the variables in terms of percentage, we will use this relationship to form more equations. As we have taken three variables, we will need three equations to solve and find the solution value of each of them.

Complete step by step solution:
Let the share of A, B, and C is a, b, and c respectively. As the amount of Rs. 2236 is shared among the three. We can say that the sum of shares of each equal Rs. 2236. In algebraic form, we can express it as $a+b+c=2236$.
We are given that the share of C is $25%$ less than the B, hence algebraically we can express it as $c=b-0.25b=0.75b$.
We are also given that the share of A is $25%$ more than C, algebraically we can express it as $a=c+0.25c=1.25c$, using the relationship between c, and b. we get $a=1.25\left( 0.75b \right)=0.9375b$.
Using these two relationships in the equation we formed $a+b+c=2236$, this can be expressed as
\begin{align} & \Rightarrow 0.9375b+b+0.75b=2236 \\ & \Rightarrow 2.6875b=2236 \\ \end{align}
Dividing both sides of the above equation by $2.6875$, we get
$\Rightarrow b=832$
Hence, the share of B is Rs. 832. We can find the share of A as,
$\Rightarrow 0.9375\left( 832 \right)=780$
Hence, the share of A is Rs. 780.

So, the correct answer is “Option C”.

Note: We can also find the share of C using the equation $c=0.75b=0.75\left( 832 \right)=624$. We can check if the answer is correct or not by substituting the values in the equation $a+b+c=2236$. Substituting the values, we get
$780+832+624=2236$