Math Problem Statement

A is 25% more than B and B is 40% less than C. if C is 20% more than D than A is what percentage less than D ?

Solution

We are given the relationships:

  1. AA is 25% more than BB, so:
    A=1.25BA = 1.25B

  2. BB is 40% less than CC, so:
    B=0.6CB = 0.6C

  3. CC is 20% more than DD, so:
    C=1.2DC = 1.2D

Step-by-step Calculation:

Express AA in Terms of DD:

  • Substitute B=0.6CB = 0.6C in A=1.25BA = 1.25B:
    A=1.25(0.6C)=0.75CA = 1.25(0.6C) = 0.75C
  • Substitute C=1.2DC = 1.2D:
    A=0.75(1.2D)=0.9DA = 0.75(1.2D) = 0.9D

Find Percentage Difference:

We need to find how much less AA is compared to DD, calculated as:

DAD×100\frac{D - A}{D} \times 100

[ \frac{D

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Percentage Increase and Decrease
Algebra

Formulas

A = 1.25B
B = 0.6C
C = 1.2D
Percentage Difference Formula: ((D - A) / D) * 100

Theorems

Percentage Change Theorem

Suitable Grade Level

Grades 9-11