Question

Production of wheat is $ 2\dfrac{1}{4} $ times that of rice but the cost of rice is $ 1\dfrac{1}{4} $ times that of wheat. If a farmer produces wheat in place of rice, then what is his income in terms of the previous income?
(a) $ 1\dfrac{4}{5} $
(b) $ \dfrac{4}{5} $
(c) $ 1\dfrac{3}{5} $
(d) $ \dfrac{3}{5} $

Answer 1

Hint: As we know that the above given question is a word problem. A problem is a mathematical question written as one sentence or more describing a real life scenario where that problem needs to be solved by the way of mathematical calculation. We can solve the given problem by applying the method of mathematical fractions but everything has to be in terms of his previous income.

Complete step-by-step answer:
We need to first understand the requirement of the question which is the income of the farmer in terms of his previous income. As per the question we have, the product of wheat is $ 2\dfrac{1}{4} $ i.e. $ \dfrac{9}{4} $ times of wheat.
Let us assume that production of rice be $ x $ quintal and cost of $ 1 $ quintal rice be $ y $ .
Now the original income of the farmer is $ x \times y = $ Rs $ xy $ . Now according to the question, the production of wheat is the $ \dfrac{9}{4} $ times of production of rice. We have the production of rice value, by substituting the values we have: $ \dfrac{9}{4}x $ quintals. Now we calculate the cost of wheat which is in terms of rice will be:
 $ 1\dfrac{1}{4} \times y = \dfrac{5}{4}y $
after reciprocating we have, $ \dfrac{4}{5}y $ .
Now the present income of farmer is
 $ \left( {\dfrac{{9x}}{4} \times \dfrac{{4y}}{5}} \right) = \dfrac{9}{5}xy $ or we can write it as $ 1\dfrac{4}{5}xy $ . So the present income of the farmer is $ 1\dfrac{4}{5} $ times of the previous income. Hence the correct option is (a) $ 1\dfrac{4}{5} $ .
So, the correct answer is “Option a”.

Note: We should always be careful what the question is asking i.e. the present income of the farmer but in terms of his previous income. Based on the requirement and by observing all the necessary information that is already available in the question we gather the information and then create an equation or by unitary method whichever is applicable, then we solve the problem and then verify the answer by putting the value in the problem and see whether we get the same answer or not.