Question

Sneha and Sidak have ${\text{Rs}}{\text{.41}}$ altogether. $\dfrac{1}{4}$ of Sneha’s money is ${\text{Rs}}{\text{.2}}$ more than $\dfrac{1}{7}$ of Sidak’s money. How much money Sneha has?
A. ${\text{Rs. 27}}{\text{.5}}$
B. ${\text{Rs. 20}}$
C. ${\text{Rs. 30}}{\text{.50}}$
D. ${\text{Rs. 29}}$

Answer 1

Hint: Let Sneha has ${\text{Rs }}x$ and Sidak has ${\text{Rs}}(41 - x)$
Now it is given that $\dfrac{1}{4}x = 2 + \dfrac{1}{7}(41 - x)$
Now solve it you will get the money of Sneha.

Complete step-by-step answer:
According to the question, Sneha and Sidak have ${\text{Rs}}{\text{.41}}$ altogether. Let Sneha have ${\text{Rs }}x$ and Sidak has ${\text{Rs}}(41 - x)$.
So Sneha has ${\text{Rs }}x$ and Sidak has ${\text{Rs}}(41 - x)$
Now one statement says that$\dfrac{1}{4}$ of Sneha’s money is $2$ more than $\dfrac{1}{7}$ of Sidak’s money. So this statement can be written in the mathematical form as:
 $\dfrac{1}{4}x = 2 + \dfrac{1}{7}(41 - x)$
Now calculating for $x$, we get that
$\dfrac{1}{4}x = 2 + \dfrac{1}{7}(41 - x)$
$\dfrac{1}{4}x = 2 + \dfrac{{41}}{7} - \dfrac{1}{7}x$
Now taking the terms consisting of $x$ on one side:
$\dfrac{1}{4}x + \dfrac{1}{7}x = 2 + \dfrac{{41}}{7}$
$\dfrac{{7x + 4x}}{{28}} = \dfrac{{14 + 41}}{7}$
$\dfrac{{11x}}{{28}} = \dfrac{{55}}{7}$
Bu cross multiplication, we get that
$x = \dfrac{{55(28)}}{{11 \times 7}} = 20$
So Sneha gets ${\text{Rs. 20}}$

So, the correct answer is “Option B”.

Note: We can also take two variables to solve this problem. So let sneha has $Rs{\text{ }}x$ and sidak has $Rs{\text{ }}y$ and we can write that $x + y = 41$ and we are also given that $\dfrac{1}{4}x = 2 + \dfrac{1}{7}(41 - x)$
Solve these equations to get the answers.