Question

Divide a rope of length $ 560\;cm $ into 2 parts such that twice the length of the smaller part is equal to $ \dfrac{1}{3} $ of the larger part. Then find the length of the larger part.

Answer 1

Hint: Here in this question we create the equations by going through the question. And we consider the system of equations and we have to solve and hence we can find the unknown parameter. Hence, we can obtain the required solution.

Complete step-by-step answer:
Now we consider the given data, by data we have the length of rope is $ 560\;cm $ . The rope has divided into two parts one is smaller and another part is larger.
Let the length of the smaller part of the rope be $ x\;cm $
The length of the larger part of the rope be $ y\;cm $
The total length of the rope is $ 560\;cm $
Therefore $ x + y = 560\;cm $ -------- (1)
By data we have the twice length of smaller part is equal to the $ \dfrac{1}{3} $ of the larger part
Therefore, we have $ 2x = \dfrac{1}{3}y $ , multiplying 3 on both sides and this can be written as $ 6x = y $ ---(2)
Consider the equation (1) and equation (2) we can rewrite the equation
 $ \Rightarrow x + 6x = 560 $
By adding we obtain
 $ \Rightarrow 7x = 560 $
Divide the equation by 7 we have
 $ \Rightarrow x = \dfrac{{560}}{7} $
And hence we have
 $ \Rightarrow x = 80 $
By substituting the value of x in equation (1) we can obtain the value of y hence we have
 $ \Rightarrow 80 + y = 560 $
On simplification we have
 $ \Rightarrow y = 560 - 80 $
 $ \Rightarrow y = 480 $
Hence, we have obtained the smaller part and the larger part and that is of length $ 80\;cm $ and $ y = 480\;cm $ .
Hence the length of the larger part is $ 480\;cm $ .
We can verify our answers by substituting x value and y value in the equation (2)
So we have
 $ 2x = \dfrac{y}{3} $
By substituting we have
 $ \Rightarrow 2(80) = \dfrac{{480}}{3} $
 $ \Rightarrow 160 = 160 $
Hence LHS = RHS and the values are the correct one which we got.
So, the correct answer is “480 cm”.

Note: Candidate should read the question and make out the relation and should write in the form of equations. If we have 2 equations we can solve the equations by substitution or cancelling and hence we can obtain the solution for the question.