Question

A sum of Rs 4830 was divided among three persons P, Q and R such that if their shares were diminished by Rs 5, Rs 10 and Rs 15 respectively the remainders would be in the ratio 3:4:5. Then P’s share would be
(a) Rs 1200
(b) Rs 1210
(c) Rs 1205
(d) Rs 1215

Answer 1

Hint: In the given question we will use the linear equation in one variable formula. Then we will take a suitable variable, say ‘x’, with each of the numbers given in the ratio. So, we will have remainders as 3x, 4x and 5x. We will consider shares as a, b, c. As per question for P, we can form the equation as a - 5 = 3x. We will do the same for Q and R also. Lastly, we will form the equation a + b + c = Rs. 4830 and substitute a, b, c in this to solve for the variable. After putting the value of the variable, we could find each of their shares.

Complete step-by-step answer:
Given, a sum of Rs 4830 is divided among three persons P, Q and R.
Let us consider for each person such as P, Q and R’s shares be ‘a’, ‘b’ and ‘c’ respectively.
According to question, we have
‘a’ is diminished (subtracted) by Rs 5
‘b’ is diminished (subtracted) by Rs 10
‘c’ is diminished (subtracted) by Rs 15
Also, given that after diminishing the remainders, that would be in the ratio 3:4:5
Let us take the remainders as 3x, 4x, 5x (whenever we get a ratio, we use variable e.g.: ‘x’ to assume their real value)
So, from above we can write for ‘a’ as,
$\begin{align}
  & \Rightarrow a-5=3x \\
 & \Rightarrow a=3x+5\cdots (i) \\
\end{align}$
Similarly, from above we can write for ‘b’ as,
 $\begin{align}
  & \Rightarrow b-10=4x \\
 & \Rightarrow b=4x+10\cdots (ii) \\
\end{align}$
Also by using the same procedure we can write for ‘c’ as
$\Rightarrow c=5x+15\cdots (iii)$
Since, sum of the money divided= Rs 4830, we get
$\Rightarrow $ P’s share + Q’s share + R’s share = Rs 4830
$\begin{align}
  & \Rightarrow a+b+c=4830 \\
 & \Rightarrow \left( 3x+5 \right)+\left( 4x+10 \right)+\left( 5x+15 \right)=4830 \\
 & \Rightarrow 12x+30=4830 \\
 & \Rightarrow 12x=4830-30 \\
 & \Rightarrow 12x=4800 \\
 & \Rightarrow x=\dfrac{4800}{12} \\
 & \Rightarrow x=400 \\
\end{align}$
Therefore, we can find P’s share:
$\begin{align}
  & \Rightarrow a=3x+5 \\
 & \Rightarrow a=3\times 400+5 \\
 & \Rightarrow a=1200+5 \\
 & \Rightarrow a=1205Rs \\
\end{align}$
Hence (c) is the correct option.

Note: This question demanded to find P’s share, if we were asked to find the shares of ‘Q’ or ‘R’; we would have used the same method and considered respective ratios to get the respective answers. In this type of question, we should mainly focus on forming the linear equation. Most of the time students go wrong while forming these linear equations. So be careful before proceeding. There is a possibility of forming the equation as a = 3x - 5 instead of a - 5 = 3x.