A student scores 25% of the total marks of a paper and fails by 30 marks. Another student scores 35% of total marks and fails by 5 marks. What is the pass mark for that paper?

Question

A bought a phone from a store and paid \(\frac{1}{6}\) of the price using UPI, \(\frac{1}{3}\) of the price in cash, and the remaining balance a year later. He also paid 10% interest on the remaining balance after one year. What was the original price of the phone?

Answer 1

The correct answer is option (C):

92.5

Here's how to solve this problem step-by-step:

Let's use variables:

* Let 'T' represent the total marks of the paper.
* Let 'P' represent the pass mark.

We can translate the given information into two equations:

* Equation 1: 0.25T = P - 30 (The first student scored 25% of the total, which is 30 marks below the pass mark.)
* Equation 2: 0.35T = P - 5 (The second student scored 35% of the total, which is 5 marks below the pass mark.)

Now we can solve for P. We can eliminate 'T' and solve for 'P'. Here's one way to do it:

1. Solve Equation 1 for T: T = (P - 30) / 0.25
2. Solve Equation 2 for T: T = (P - 5) / 0.35
3. Since both equations equal T, we can set them equal to each other: (P - 30) / 0.25 = (P - 5) / 0.35
4. Cross-multiply: 0.35(P - 30) = 0.25(P - 5)
5. Distribute: 0.35P - 10.5 = 0.25P - 1.25
6. Subtract 0.25P from both sides: 0.1P - 10.5 = -1.25
7. Add 10.5 to both sides: 0.1P = 9.25
8. Divide both sides by 0.1: P = 92.5

Therefore, the pass mark for that paper is 92.5.

A student scores 25% of the total marks of a paper and fails by 30 marks. Another student scores 35% of total marks and fails by 5 marks. What is the pass mark for that paper?

The Correct Option is C

Solution and Explanation

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