Percentage

I. Four friends studying in different schools sat down to discuss their scores in their mid-term examinations. Their scores are as under:

i. A secured 56 marks out of 80.

ii. B secured 108 marks out of 150.

iii. C secured 51 marks out of 75.

iv. D secured 87 marks out of 120.

Q1: Which of the four friends had the best performance?

Step 1: Convert each score to percentage:
A = \(\frac{56}{80} \times 100 = 70\%\)
B = \(\frac{108}{150} \times 100 = 72\%\)
C = \(\frac{51}{75} \times 100 = 68\%\)
D = \(\frac{87}{120} \times 100 = 72.5\%\)
Step 2: Highest percentage = 72.5% → D
Answer: d. D

Q2: C got his test paper re-evaluated and his score increased by 12%. His new score is:

Step 1: C’s original score = 51
Increase = 12% of 51 = \(\frac{12}{100} \times 51 = 6.12\)
New score = \(51 + 6.12 = 57.12\)
Step 2: Closest to option: ≈ 57.5
Answer: b. 57.5

Q3: If the pass percentage in A’s test was 40%, how many percent more marks did he obtain than the passing marks?

Step 1: Passing marks = 40% of 80 = \(0.4 \times 80 = 32\)
Marks obtained = 56
Excess = \(56 – 32 = 24\)
Step 2: Percentage more than passing = \(\frac{24}{32} \times 100 = 75\%\)
Answer: d. 75%

Q4: If D obtained 45 marks more than the passing marks, then what was the pass percentage in his test?

Step 1: Marks obtained = 87
Let passing marks = x
Then \(87 = x + 45 \Rightarrow x = 42\)
Step 2: Total marks = 120
Pass percentage = \(\frac{42}{120} \times 100 = 35\%\)
Answer: b. 35%