Aman’s salary is first increased by 25% and then decreased by 20%. The result is the same as Baman’s salary increased by 20% and then reduced by 25%..

Aman’s salary is first increased by 25% and then decreased by 20%. The result is the same as Baman’s salary increased by 20% and then reduced by 25%. Find the ratio of Baman’s initial salary to that of Aman’s initial salary.

The Correct answer is 10:9

Explanation

Calculate Aman's final salary:

First, his salary increases by 25%: x * (1 + 25/100) = 1.25x

Then, it decreases by 20%: 1.25x * (1 - 20/100) = 1.25x * 0.8 = x

Calculate Baman's final salary:

Let Baman's initial salary be y.

Baman's salary first increases by 20%: y * (1 + 20/100) = 1.2y

Then, it decreases by 25%: 1.2y * (1 - 25/100) = 1.2y * 0.75 = 0.9y

Set up the equation based on the given condition:

As per the problem, Aman's final salary (after the increase and decrease) is equal to Baman's final salary:

Equation: x = 0.9y

Solve for the ratio:

We want to find the ratio of Baman's initial salary (y) to Aman's initial salary (x). Divide both sides of the equation by x:

• 1 = 0.9y / x

• Taking the reciprocal of both sides: x/y = 1 / 0.9

Therefore, the ratio of Baman's initial salary (y) to Aman's initial salary (x) is 10:9.

This means Baman's initial salary is 10/9 times bigger than Aman's initial salary.

Ratio

In mathematics, a ratio is a relationship between two numbers indicating how many times one number contains or is contained within the other. Ratios are typically expressed as a fraction or with a colon between the two numbers. For example, if there are 3 red balls and 5 blue balls in a bag, the ratio of red balls to blue balls is 3:5.

Ratios can be used to compare quantities of the same type, such as lengths, weights, or amounts of money. They are often simplified to their simplest form, where the two numbers have no common factors other than 1. For example, the ratio 6:10 can be simplified to 3:5.

Ratios are used in various mathematical contexts, including proportions, rates, and scale drawings. They are also used in everyday situations, such as cooking (recipe ratios), financial planning, and comparing sizes or quantities.