Question

An umbrella and a bag together cost Rs152. If the price of the bag is Rs24 more than that of the umbrella. What would be the cost of 6 such bags?

Answer 1

Hint: First of all, let the cost of the umbrella be x and the cost of the bag be y and then form an equation using this. Now, the cost of bag (y) is Rs24 more than the cost of umbrella (x). So, if we add 34 to x, it will be equal to y. Substitute this value of y in the first equation and we will get the values of x and y. Now, to find the cost of 6 bags, multiply the value of y with 6.

Complete step-by-step answer:
In this question, we are given an umbrella and a bag. The cost of both these together is Rs152. Now, it is given that the cost of a bag is more than that of an umbrella by Rs24. So, we need to find the cost of 6 such bags.
Here, let the cost of the umbrella be x and the cost of bag be y.
 $ \Rightarrow $ Cost of umbrella $ = x $
 $ \Rightarrow $ Cost of bag $ = y $
Therefore,
 $ \Rightarrow x + y = 152 $ - - - - - - (1)
Now, we are given that the cost of a bag (y) is Rs24 more than the cost of umbrella (x). Therefore, we can write it in equation form as
 $ \Rightarrow y = 24 + x $ - - - - - - (2)
So, now we can substitute $ y = 24 + x $ in equation (1) and get
 $
   \Rightarrow x + y = 152 \\
   \Rightarrow x + \left( {24 + x} \right) = 152 \\
   \Rightarrow x + x = 152 - 24 \\
   \Rightarrow 2x = 128 \\
   \Rightarrow x = \dfrac{{128}}{2} \\
   \Rightarrow x = 64 \;
  $
Hence, the cost of umbrella is Rs64.
Now, substituting this in equation (2), we get
 $
   \Rightarrow y = 24 + x \\
   \Rightarrow y = 24 + 64 \\
   \Rightarrow y = 88 \;
  $
Hence, the cost of bag is Rs88.
Now, we have to find the cost of 6 such bags. So, for that we are going to use the method of cross multiplication.
 $
  1bag = Rs88 \\
  6bags = ? \\
  $
Therefore,
 $ \Rightarrow $ Cost of 6 bags $ = \dfrac{{88 \times 6}}{1} = 528 $
Hence, the cost of 6 such bags will be Rs528.
So, the correct answer is “Rs 528”.

Note: Here, we can also solve the two equations by using the elimination method.
 $ \Rightarrow x + y = 152 $ - - - - - (1)
 $ \Rightarrow y = 24 + x $
 $ \Rightarrow x - y = - 24 $ - - - - - (2)
So, subtracting equation (2) from equation (1), we get
 $
  \underline
  x + y = 152 \\
   - x + y = + 24 \\
    \\
  0 + 2y = 176 \\
   \Rightarrow y = \dfrac{{176}}{2} \\
   \Rightarrow y = 88 \\
  $
Now, substituting $ y = 88 $ in equation (2), we get
 $
   \Rightarrow x - y = - 24 \\
   \Rightarrow x - 88 = - 24 \\
   \Rightarrow x = - 24 + 88 \\
   \Rightarrow x = 64 \;
  $