Question

In a joint family the capitals invested by Laxmi and Saraswati are in the ratio 7: 5 and the ratio of their profits is 4:3. If Laxmi’s capital was invested for 20 months then how much time Saraswati capital would have been invested?
(a) 21 months
(b) 30 months
(c) 40 months
(d) 15 months

Answer 1

Hint: Here, we will use the concept that the profit on the capital invested by Laxmi and Saraswati is equal to the product of the capital invested by them with the time for which the capital is invested. We will assume Saraswati’s capital to be y and then find her profit in terms of y. Then, we will equate the ratio of Laxmi’s profit to Saraswati’s profit to 4:3 to get the value of y.

Complete step-by-step answer:
Let us consider that Saraswati invested the capital for ‘y’ months.
Now, it is given that the ratio of the capitals invested by Laxmi and Saraswati is 7:5.
So, let us consider that Laxmi’ capital is = 7x.
And, Saraswati’s capital is = 5x.
Since, Laxmi’s capital is invested for 20 months, so profit on Laxmi’s capital is = $7x\times 20$
Also, as we have considered that Saraswati’s capital is invested for ‘y’ months, so profit on Saraswati’s capital is = \[5x\times y\]
Since, the ratio of their profit is given as 4:3.
Therefore, we can write as:
$\dfrac{7x\times 20}{5x\times y}=\dfrac{4}{3}$
On cancelling x from both the numerator and denominator on the left side of the equation, we get:
$\dfrac{7x\times 20}{5x\times y}=\dfrac{4}{3}$
Here, on doing cross multiplication, we get:
$3\left( 7\times 20 \right)=4\times \left( 5\times y \right)$
$\Rightarrow 3\times 7\times 20=20\times y$
On dividing both sides of the equation by 20, we get:
$\begin{align}
  & 3\times 7=y \\
 & \Rightarrow y=21 \\
\end{align}$
So, the value of y comes out to be 21.
Therefore, saraswati capital is invested for 21 months.
Hence, option (a) is the correct answer.

Note: It should be kept in mind that we have been given the ratio of Laxmi’s profit to Saraswati’s profit. So, we have to always keep in mind the numerator and Saraswati’s profit in the denominator if we are equating it to 4:3. If the numerator and denominator are exchanged, the ratio would be 3:4. Doing this will give us decimal values. When we compare with options, we will not be able to find such an option. So, this whole process will in effect delay the time spent on one question in the exam.