In a test, Rakhesh got 50% marks and scored 10 marks more than the pass marks. In the same test, Suresh secured 55% marks and scored 20 marks more than the pass marks. Find the pass marks.

To solve the problem of finding the pass marks based on Rakhesh's and Suresh's scores, we can set up equations based on the information given. Let’s break it down step by step.

Setting Up the Problem

Let’s denote the total marks of the test as T and the pass marks as P.

Information from Rakhesh's Score

Rakhesh scored 50% of the total marks, which can be expressed as:

• Rakhesh's score = 0.5T

According to the problem, Rakhesh scored 10 marks more than the pass marks:

• 0.5T = P + 10

Information from Suresh's Score

Suresh scored 55% of the total marks, represented as:

• Suresh's score = 0.55T

Similarly, Suresh scored 20 marks more than the pass marks:

• 0.55T = P + 20

Creating the Equations

Now we have two equations based on the information provided:

• 1. 0.5T = P + 10
• 2. 0.55T = P + 20

Solving the Equations

We can rearrange both equations to express P in terms of T.

• From the first equation: P = 0.5T - 10
• From the second equation: P = 0.55T - 20

Since both expressions equal P, we can set them equal to each other:

• 0.5T - 10 = 0.55T - 20

Isolating T

Now, let’s solve for T:

• Rearranging gives: 20 - 10 = 0.55T - 0.5T
• 10 = 0.05T
• T = 10 / 0.05
• T = 200

Finding the Pass Marks

Now that we have the total marks T, we can substitute it back into one of our equations to find P. Using the first equation:

• P = 0.5(200) - 10
• P = 100 - 10
• P = 90

Final Result

The pass marks for the test are 90 marks.

To summarize, by setting up equations based on the percentages and the additional marks above the pass marks, we were able to find that the pass marks are 90. This method of using algebra to solve for unknowns is very effective in problems like these!