Question

Karim caught 3 times as much fish as Rani did. Altogether, they caught 24 fish. How many fish did Rani catch?

Answer 1

Hint: We can take the number of fish each of them caught as 2 variables. Then we can do one as three times as given in the question. We can then take the sum as given. Then we can solve the equation to get the required number of fishes.

Complete step-by-step answer:
Let x be the number of fishes caught by Karim and y be the number of fishes caught by Rani.
It is given that Karim caught 3 times as much fish as Rani did. So, in terms of the variable, we can write it as,
 $ \Rightarrow x = 3y$ … (1)
It is given that they altogether caught 24 fishes. It can be written as the sum of the 2 variables.
 $ \Rightarrow x + y = 24$ .. (2)
Now we can solve the equations (1) and (2).
We can substitute equation (1) in (2)
 $ \Rightarrow 3y + y = 24$
On simplification, we get,
 $ \Rightarrow 4y = 24$
On dividing throughout with 4, we get,
 $ \Rightarrow y = \dfrac{{24}}{4}$
On simplification we get,
 $ \Rightarrow y = 6$
From our assumption, the number of fishes that Rani caught is y.
Therefore, the number of fishes that Rani caught is 6.

Note: Alternate method to solve this problem is by taking the ratios.
It is given that Karim caught 3 times as much fish as Rani did.
So, the ratio of fish caught by Karim to Rani is $3:1$ .
We can multiply the ratio with a variable x.
 $ \Rightarrow 3x:1x$
It is given that they altogether caught 24 fishes.
We can multiply the ratio with a variable x and equate its sum to 24.
 $ \Rightarrow 3x + x = 24$
On simplification we get,
 $ \Rightarrow 4x = 24$
On dividing throughout with 4, we get,
 $ \Rightarrow x = \dfrac{{24}}{4}$
On simplification we get,
 $ \Rightarrow x = 6$
Substituting back in the ratio, we get the number of fishes that Rani caught is 1x.
Therefore, the number of fishes that Rani caught is 6.