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). 460
(B). 484
(C). 550
(D). 664

Answer 1

Hint: In these types of questions you can use the method of ratio proportion or the method of linear equation and also remember to find the value of x or y with respect to y or x, use this information to approach the solution of the question.

Complete step-by-step answer:
According to the given information
We know that the A and B together have Rs. 1210 where $\dfrac{4}{{15}}$ amount of A is equal to $\dfrac{2}{5}$ amount of B
First using the method of ratio proportion
It is given that \[\dfrac{4}{{15}}A = \dfrac{2}{5}B\]
$ \Rightarrow $\[A = \dfrac{{15}}{4} \times \dfrac{2}{5}B\]
$ \Rightarrow $\[A = \dfrac{3}{2}B\]
$ \Rightarrow $\[\dfrac{A}{B} = \dfrac{3}{2}\]
So A: B = 3: 2
We know that to find the share of B the formula used is $\dfrac{B}{{A + B}}$
Substituting the value in the above formula we get
Amount of B has = $\dfrac{2}{{3 + 2}}$
$ \Rightarrow $ Amount of B has = $\dfrac{2}{5}$
Therefore total amount of B = $\dfrac{2}{5} \times 1210$
$ \Rightarrow $Total amount of B = Rs. 484
Therefore B will have Rs. 484
Hence option B is the correct option.

Note:The above problem can be also solved using linear equation method
So according to the given information we know that amount of B and amount of A is equal to Rs. 1210
So let x be the amount of A and y be the amount of B
Therefore x + y = 1210 (equation 1)
Also it is given that $\dfrac{4}{{15}}$ amount of A is equal to $\dfrac{2}{5}$ amount of B
Therefore $\dfrac{4}{{15}}$x = $\dfrac{2}{5}$y
$ \Rightarrow $\[x = \dfrac{3}{2}y\]
Substituting the value of x in the equation 1 we get
\[\dfrac{3}{2}y\]+ y = 1210
$ \Rightarrow $\[\dfrac{3}{2}y\]+ y = 1210
$ \Rightarrow $\[\dfrac{{3y + 2y}}{2}\] = 1210
$ \Rightarrow $5y = 2(1210)
$ \Rightarrow $5y =2420
$ \Rightarrow $$y = \dfrac{{2420}}{5}$
$ \Rightarrow $y = 484
As we know that y is the amount of B therefore
Rs. 484 is the amount B contains.