
The price of a car is lowered by \[20\% \] to Rs. 40,000. What was the original price?
Answer
140.1k+ views
Hint: Here, we will first assume the original price and then find the value of the reducing price using the original price. Then calculate the difference of reducing price from the original price of a car and take this difference equal to the reduced price to find the original price.
Complete step-by-step solution
Let us assume that the original price is Rs. \[x\].
We will first find the value of reducing price of a car lowered by \[20\% \] in terms of \[x\].
\[\dfrac{{20}}{{100}}x\]
Now we will calculate the original price of a car, which was lowered to Rs. 40,000 by subtracting the reducing price from the original price.
\[
\Rightarrow x - \dfrac{{20}}{{100}}x = 40000 \\
\Rightarrow \dfrac{{100x - 20x}}{{100}} = 40000 \\
\Rightarrow \dfrac{{80x}}{{100}} = 40000 \\
\]
Multiplying the above equation by 100 on each of the sides, we get
\[
\Rightarrow \dfrac{{80x}}{{100}} \times 100 = 40000 \times 100 \\
\Rightarrow 80x = 4000000 \\
\]
Dividing the above equation by 80 on both sides, we get
\[
\Rightarrow \dfrac{{80x}}{{80}} = \dfrac{{4000000}}{{80}} \\
\Rightarrow x = 50000 \\
\]
Thus, the original price of a car is Rs. 50000.
Note: In these types of questions, we first assume the original price as any variable and then find the reducing price using the original price. In this question, some students find the sum of the reducing price and original price, which is wrong, we always have to find the difference as the prices are lowered.
Complete step-by-step solution
Let us assume that the original price is Rs. \[x\].
We will first find the value of reducing price of a car lowered by \[20\% \] in terms of \[x\].
\[\dfrac{{20}}{{100}}x\]
Now we will calculate the original price of a car, which was lowered to Rs. 40,000 by subtracting the reducing price from the original price.
\[
\Rightarrow x - \dfrac{{20}}{{100}}x = 40000 \\
\Rightarrow \dfrac{{100x - 20x}}{{100}} = 40000 \\
\Rightarrow \dfrac{{80x}}{{100}} = 40000 \\
\]
Multiplying the above equation by 100 on each of the sides, we get
\[
\Rightarrow \dfrac{{80x}}{{100}} \times 100 = 40000 \times 100 \\
\Rightarrow 80x = 4000000 \\
\]
Dividing the above equation by 80 on both sides, we get
\[
\Rightarrow \dfrac{{80x}}{{80}} = \dfrac{{4000000}}{{80}} \\
\Rightarrow x = 50000 \\
\]
Thus, the original price of a car is Rs. 50000.
Note: In these types of questions, we first assume the original price as any variable and then find the reducing price using the original price. In this question, some students find the sum of the reducing price and original price, which is wrong, we always have to find the difference as the prices are lowered.
Recently Updated Pages
Difference Between Mutually Exclusive and Independent Events

Difference Between Area and Volume

JEE Main 2025 (Session 2) April 3 Shift 1 Exam Analysis and Solutions FREE PDF

JEE Main 2025 Session 2 (April 3 Shift 1) Mathematics Paper Analysis with Solutions

JEE Mains 2025 April 3 Shift 1 Question Paper Live Updates for Physics

JEE Main 2025 April 3 Shift 1: Chemistry Question Paper PDF and Analysis

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main Syllabus 2025 (Updated)

JEE Main Question Papers 2025

JEE Main Marks Vs Percentile Vs Rank 2025: Calculate Percentile Using Marks

JEE Mains 2025 Cutoff: Expected and Category-Wise Qualifying Marks for NITs, IIITs, and GFTIs

Raoult's Law with Examples

Other Pages
NCERT Solutions for Class 9 Maths Chapter 11 Surface Area and Volume

NCERT Solutions for Class 9 Maths Chapter 11 Surface Areas And Volumes Ex 11.3

NCERT Solutions for Class 9 Maths Chapter 9 Circles

NCERT Solutions for Class 9 Maths Chapter 12 Statistics

NCERT Solutions for Class 9 Maths Chapter 10 Heron'S Formula

NCERT Solutions for Class 9 Maths In Hindi Chapter 1 Number System
