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Cricket/Marks Average Problems

Introduction

Aptitude tests में cricket/marks average problems बहुत common होते हैं। ऐसे questions में अक्सर missing score, total runs/marks, या किसी player/student का overall performance निकालना होता है।

Trick हमेशा यही है कि average formula सही तरह apply करें: Average = Total ÷ Number of terms.

Pattern: Cricket/Marks Average Problems

Pattern

Main idea: Average से total निकालें या total से average - फिर missing data भरें।

Steps:
1. Formula लिखें: Total = Average × Number of terms.
2. Known scores/runs subtract करके missing score निकालें।
3. या नया score जोड़कर updated average निकालें।

Step-by-Step Example

Question

एक cricketer ने 9 innings में average 50 runs बनाए हैं। 10th inning में उसे कितने runs बनाने होंगे ताकि उसका नया average 55 हो जाए?

Options:
A. 80 runs
B. 90 runs
C. 100 runs
D. 110 runs

Solution

  1. Step 1: 9 innings का total runs निकालें

    Total = 9 × 50 = 450.

  2. Step 2: 10 innings के लिए required total

    New total = 10 × 55 = 550.

  3. Step 3: 10th inning में required runs

    Required = 550 - 450 = 100.

  4. Final Answer:

    100 runs → Option C

  5. Quick Check:

    (450 + 100) ÷ 10 = 55 ✅

Quick Variations

Marks Problems:

- 5 subjects का average 60 हो तो total = 60 × 5 = 300.

- 4 subjects के marks दिए हों तो missing 5th = 300 - (known marks).

Updating Averages:

- नया match/subject add होने पर total update करें और new count से divide करें।

Trick to Always Use

  • Step 1: Average × Count = Total निकालें।
  • Step 2: Known scores subtract/add करें।
  • Step 3: Updated average पाने के लिए divide करें।

Summary

Summary

Cricket/Marks Average Problems में सबसे पहले Total = Average × Number of terms use करें। इससे missing runs/marks या नया average seconds में निकल जाता है।

  • Average → Total convert करें जब count दिया हो।
  • Missing score = Required total - Known total.
  • New entry जोड़ने पर total update करें और average निकालें।

Practice

(1/5)
1. A student scores an average of 60 marks in 4 subjects. If his marks in three subjects are 58, 62, and 64, find his marks in the fourth subject.
easy
A. 56
B. 60
C. 64
D. 68

Solution

  1. Step 1: Compute total marks

    Total marks = 60 × 4 = 240.

  2. Step 2: Compute known marks total

    Sum of three subjects = 58 + 62 + 64 = 184.

  3. Step 3: Find missing marks

    Fourth subject = 240 - 184 = 56.

  4. Final Answer:

    56 → Option A

  5. Quick Check:

    (58 + 62 + 64 + 56) ÷ 4 = 240 ÷ 4 = 60 ✅
Hint: Multiply average by count to get total, then subtract known marks.
Common Mistakes: Forgetting to multiply average by the number of subjects before subtracting.
2. A batsman has scored 360 runs in 9 innings. What must he score in the 10th inning to increase his average by 5 runs?
medium
A. 85
B. 90
C. 95
D. 100

Solution

  1. Step 1: Compute current average

    Current average = 360 ÷ 9 = 40.

  2. Step 2: Compute new average

    Required average = 40 + 5 = 45.

  3. Step 3: Compute required total

    Total runs needed for 10 innings = 10 × 45 = 450.

  4. Step 4: Compute required 10th inning score

    Runs required in 10th inning = 450 - 360 = 90.

  5. Final Answer:

    90 → Option B

  6. Quick Check:

    (360 + 90) ÷ 10 = 450 ÷ 10 = 45 ✅
Hint: Compute required total from new average and subtract existing total.
Common Mistakes: Adding the increase directly to the last score instead of adjusting the total.
3. The average score of 8 students in an exam is 72. If one student’s score of 64 is replaced by 80, what is the new average?
medium
A. 73
B. 74
C. 75
D. 76

Solution

  1. Step 1: Compute original total

    Original total = 8 × 72 = 576.

  2. Step 2: Compute change in total

    Replacement increases total by 80 - 64 = 16.

  3. Step 3: Compute new total

    New total = 576 + 16 = 592.

  4. Step 4: Compute new average

    New average = 592 ÷ 8 = 74.

  5. Final Answer:

    74 → Option B

  6. Quick Check:

    Increase per student = 16 ÷ 8 = 2 → 72 + 2 = 74 ✅
Hint: Adjust the old total by the change, then divide by the same count.
Common Mistakes: Recomputing all scores instead of applying the net change method.
4. The average score of 10 innings of a batsman is 32. How many runs must he score in the next inning to raise the average to 35?
medium
A. 60
B. 62
C. 65
D. 68

Solution

  1. Step 1: Compute current total

    Current total = 10 × 32 = 320.

  2. Step 2: Compute required total

    Required total for 11 innings = 11 × 35 = 385.

  3. Step 3: Compute required runs

    Runs needed = 385 - 320 = 65.

  4. Final Answer:

    65 → Option C

  5. Quick Check:

    (320 + 65) ÷ 11 = 385 ÷ 11 = 35 ✅
Hint: Required runs = (new average × new count) - old total.
Common Mistakes: Forgetting to include the new inning in the count when calculating the new total.
5. A student has an average of 70 marks in 6 subjects. If he scores 88 in the seventh subject, what is his new average (to two decimal places)?
medium
A. 72
B. 72.5
C. 72.57
D. 73

Solution

  1. Step 1: Compute original total

    Original total = 6 × 70 = 420.

  2. Step 2: Compute new total

    New total = 420 + 88 = 508.

  3. Step 3: Compute new average

    New average = 508 ÷ 7 = 72.571428.... To two decimal places this is 72.57.

  4. Final Answer:

    72.571428... → Option C (72.57 to two decimal places).

  5. Quick Check:

    Increase = 88 - 70 = 18 → Increase per subject = 18 ÷ 7 ≈ 2.5714 → 70 + 2.5714 ≈ 72.5714 ✅
Hint: Add the new mark to the old total and divide by the new count; express to required decimal places.
Common Mistakes: Rounding too early or misplacing the divisor when computing the new average.

Mock Test

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