A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a beggar waiting outside the shop. She spent half of what was left on lunch and followed that up with a two rupee tip. She spent half of the remaining amount on a book and three rupees on bus fare. When she reached home, she found that she had exactly one rupee left. How much money did she start with?
Answer
279.9k+ views
Hint: In this problem the lady spends money sequentially at different spaces. She spends a fraction of what is left on next purchase. This is the problem that will take us into a fractional equation giving the last solution that is money left one rupee.
Try to solve the problem along with the journey of the lady.
Complete step-by-step answer:
Consider the amount lady had initially $ = x\,\,Rupees$
First, she spent half she had for hankie and gave one rupee to the beggar
Money spent:
= $ \dfrac{x}{2} + 1$
Money left:
$
= x - \left( {\dfrac{x}{2} + 1} \right) \\
\Rightarrow \dfrac{x}{2} - 1 \;
$
Second, she spent half left on lunch with two rupee tip
Money spent:
\[
\Rightarrow \dfrac{{\dfrac{x}{2} - 1}}{2} + 2 \\
\Rightarrow \dfrac{x}{4} + \dfrac{3}{2} \;
\]
Money left:
$ $ \[
\Rightarrow \dfrac{x}{2} - 1 - \left( {\dfrac{x}{4} + \dfrac{3}{2}} \right) \\
\Rightarrow \dfrac{x}{4} - \dfrac{5}{2} \;
\]
Third, purchase she spent half of what was left on a book and 3 rupees on bus fare
Money Spent:
$
\Rightarrow \left( {\dfrac{{\dfrac{x}{4} - \dfrac{5}{2}}}{2} + 3} \right) \\
\Rightarrow \dfrac{x}{8} + \dfrac{7}{4} \;
$
Money left:
\[
\Rightarrow \dfrac{x}{4} - \dfrac{5}{2} - \left( {\dfrac{x}{8} + \dfrac{7}{4}} \right) \\
\Rightarrow \dfrac{x}{8} - \dfrac{{17}}{4} \;
\]
Money she left with is one rupee
\[
\Rightarrow \dfrac{x}{8} - \dfrac{{17}}{4} = 1 \\
\Rightarrow \dfrac{x}{8} = \dfrac{{21}}{4} \\
\Rightarrow x = 42\,Rupees \;
\]
Hence, she had 42 rupees at the start of the journey.
So, the correct answer is “42 rupees”.
Note: The concept of fraction is widely used in many areas like calculating age, estimating profit loss, getting the share of profit of one among the three, etc. The simplification involves all mathematical operations on one variable. The use of multiple operations makes the problem tricky.
Try to solve the problem along with the journey of the lady.
Complete step-by-step answer:
Consider the amount lady had initially $ = x\,\,Rupees$
First, she spent half she had for hankie and gave one rupee to the beggar
Money spent:
= $ \dfrac{x}{2} + 1$
Money left:
$
= x - \left( {\dfrac{x}{2} + 1} \right) \\
\Rightarrow \dfrac{x}{2} - 1 \;
$
Second, she spent half left on lunch with two rupee tip
Money spent:
\[
\Rightarrow \dfrac{{\dfrac{x}{2} - 1}}{2} + 2 \\
\Rightarrow \dfrac{x}{4} + \dfrac{3}{2} \;
\]
Money left:
$ $ \[
\Rightarrow \dfrac{x}{2} - 1 - \left( {\dfrac{x}{4} + \dfrac{3}{2}} \right) \\
\Rightarrow \dfrac{x}{4} - \dfrac{5}{2} \;
\]
Third, purchase she spent half of what was left on a book and 3 rupees on bus fare
Money Spent:
$
\Rightarrow \left( {\dfrac{{\dfrac{x}{4} - \dfrac{5}{2}}}{2} + 3} \right) \\
\Rightarrow \dfrac{x}{8} + \dfrac{7}{4} \;
$
Money left:
\[
\Rightarrow \dfrac{x}{4} - \dfrac{5}{2} - \left( {\dfrac{x}{8} + \dfrac{7}{4}} \right) \\
\Rightarrow \dfrac{x}{8} - \dfrac{{17}}{4} \;
\]
Money she left with is one rupee
\[
\Rightarrow \dfrac{x}{8} - \dfrac{{17}}{4} = 1 \\
\Rightarrow \dfrac{x}{8} = \dfrac{{21}}{4} \\
\Rightarrow x = 42\,Rupees \;
\]
Hence, she had 42 rupees at the start of the journey.
So, the correct answer is “42 rupees”.
Note: The concept of fraction is widely used in many areas like calculating age, estimating profit loss, getting the share of profit of one among the three, etc. The simplification involves all mathematical operations on one variable. The use of multiple operations makes the problem tricky.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How many meters are there in a kilometer And how many class 8 maths CBSE

What is pollution? How many types of pollution? Define it

Change the following sentences into negative and interrogative class 10 english CBSE

What were the major teachings of Baba Guru Nanak class 7 social science CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Draw a labelled sketch of the human eye class 12 physics CBSE
