Question

A and B together have Rs. 1210. If $\dfrac{4}{15}$ of A’s amount is equal to $\dfrac{2}{5}$ of B’s amount. How much amount does B have?
(a) Rs. 484
(b) Rs. 184
(c) Rs. 550
(d) Rs. 664

Answer 1

Hint: Here, we may take the amounts that A and B have as variables x and y respectively. After that we can form equations using the given conditions to obtain the values of x and y.

Complete step by step solution:

Let us consider the amount that A is having = Rs. x
And the amount that B is having = y
Since, it is given that A and B together have a total amount of Rs. 1210.
So, we can write the following equation:
x + y = 1210……….(1)
Also, it is given that $\dfrac{4}{15}$ of the amount that A has is equal to the $\dfrac{2}{5}$ of the amount that B has.
So, according to this we can write the following equation:
$\begin{align}
  & \dfrac{4}{15}\times x=\dfrac{2}{5}\times y \\
 & \dfrac{4}{15}\times x\times 5=2y \\
 & 4x=6y \\
\end{align}$
On dividing both sides of the equation by 2, we get:
$2x=3y.........(2)$
Now, from equation we can also write:
$y=\left( 1210-x \right)$
On substituting this value of y in equation (2), we get:
2x = 3( 1210-x )
2x = 3630 – 3x
2x +3x = 3630
5x = 3630
$x=\dfrac{3630}{5}=726$
So, the value of x is = 726. It means that A has an amount of Rs. 726.
On substituting the value x = 726 in equation (1), we get:
726 + y = 1210
y = 1210 – 726
 y = 484
So, the value of y is 484. It means that B is having an amount of Rs. 484.
Hence, option (a) is the correct answer.

Note: Equations should be formed properly according to the question to avoid mistakes. Here, it is not necessary to solve for x, since A’s amount is not asked in the question. So, we can solve it directly for y to get only the B’s amount.