Question

A table costs $ Rs200 $ more than a chair. The price of two tables and three chairs is $ 1400 $ . Find the Cost Price of the table.

Answer 1

Hint: From the question it is easy to understand that it is a sum from the chapter Simultaneous Equation. First Step in solving Simultaneous equations is defining the Variables correctly. After defining the variables we need to interpret the statements correctly and form an equation. It is necessary that we understand the statements properly. Though we get an answer after solving the equation they might not be correct if our interpretation is wrong.

Complete step-by-step answer:
Let Cost of $ 1 $ table be $ RsT $ .
Let the Cost of $ 1 $ Chair be $ RsC $ .
From the first statement we can interpret that cost of $ 1 $ table is $ Rs200 $ more than a chair, we can form a equation with the given data using these two variables and a constant
 $ T = 200 + C...................(1) $
With the help of 2nd sentence we can form the following equation:
 $ 2T + 3C = 1400.................(2) $
Now we can substitute the value of $ T $ from $ Equation1 $ and substitute in the $ Equation2 $ in order to get the value of $ C $ . After finding the Value of $ C $ we can substitute in $ Equation1 $ to find the value of $ T $ .
 $ \Rightarrow 2 \times (200 + C) + 3C = 1400...........(3) $
 $ \Rightarrow 2C + 400 + 3C = 1400........(4) $
 $ \Rightarrow 5C = 1400 - 400.......(5) $
 $ \Rightarrow C = 200..........(6) $
Using the value of $ C $ from $ Equation6 $ and substituting in $ Equation1 $ we will get the value of $ T $
 $
   \Rightarrow T = 200 + 200 \\
   \Rightarrow T = 400 \;
 $
The Price of $ 1 $ table is $ Rs400 $
So, the correct answer is “ $ Rs400 $ ”.

Note: Since it is easy we have substituted the value of $ T $ in $ Equation2 $ and found out the answer. In case of a difficult numerical it makes sense to solve the Equations simultaneously in order to make the sum easier. We need to always keep in mind that though these types of word problems seem difficult to solve sometimes, if we pick up each statement and then form an equation accordingly it would make the problem extremely easy to solve within a Minute.