Maths-1 Average: Questions and Step-by-Step Solutions for Competitive Exams SSC, BSSC, Bank,Railways)

Maths-1 Average : Question and Step-by-Step Solutions for Competitive Exams (SSC, BSSC, Bank, Railways) Step-by-Step Solutions

Average questions in Mathematics. Covers basics, missing numbers, combined groups, and speed-based problems. Ideal for SSC, Bank, Railways, and competitive exam preparation

Maths-1 Average

1. What is Average?

👉 Average means the “equal share” or “middle value” of a set of numbers.

The formula is:

Average=Number of observations/Sum of all observations​

2. Step-by-step Examples

Example 1: Very Basic

The marks of a student in 3 subjects are: 40, 50, 60.
Find the average.

Solution:

Sum=40+50+60=150

Number of observations=3

Average=150/3=50

✔ Answer = 50

Example 2: Daily life use

A man travels 20 km, 25 km, and 35 km on three days. Find his average distance.

Solution:

Sum=20+25+35=80

Average=80/3=26.67 km (approx.)

✔ Answer = 26.67 km

3. Shortcut Ideas

Sometimes instead of adding everything, you can use adjustment method.

Example 3: Adjustment Method

Find the average of 48, 50, 52, 54.

👉 Middle value is 51, and numbers are equally spread.
So, average = 51 (no need to calculate full sum).

4. Weighted Average (Important in exams)

If different items have different “weights” (importance), we use weighted average.

Example 4: Weighted Average

A student scores:

• 80 in Maths (weight 3)
• 70 in Science (weight 2)
• 60 in English (weight 1)

Find average marks.

Solution:

Weighted sum=(80×3)+(70×2)+(60×1)=240+140+60=440 Total weights=3+2+1=6

Average} =440/6 = 73.33

✔ Answer = 73.33

5. Important Types of Average Questions in Exams

1. Simple average (direct formula).
2. Average after adding/removing a number.
3. Finding a missing number if average is given.
4. Average of combined groups.
5. Speed & average problems (special formula).

 Let’s cover the special average problems you’ll see in exams, step-by-step and with worked examples. I’ll start with a very quick refresher, then move to the special cases (missing number, combined groups, adding/removing numbers, weighted average, and speed problems). After each concept you’ll get one worked example (fully shown digit-by-digit) so there’s no arithmetic slip.

Quick refresher

Average (arithmetic mean) of n numbers x1,……,xn​:

Average=x1+x2+⋯+xn / n​​

So often the first step is convert an average statement into a sum: sum=average×count

sum=average×count.

6) Missing number (one number unknown)

Idea: If average of nnn numbers is AAA, total sum = A×n. Subtract the known numbers to get the missing one.

Example: Average of 5 numbers is 20. Four numbers: 18, 22, 20, 24. Find the 5th.

Step-by-step:

1. Total for 5 numbers =20×5=100.
2. Sum of known four: 18+22=40 ; 40+20=60 ; 60+24=84
3. Missing number =100−84=16.

Answer: 16

7) Combined groups (two groups merged)

Idea: Compute each group’s total (average × count), add totals and divide by total people.

Example: Class A: 20 students, avg 72. Class B: 30 students, avg 68. Combined average?

Step-by-step:

1. Sum A =72×20=72 Compute: 72×20=72×(2×10)=144×10=1440.
2. Sum B =68×30 Compute: 68×30=68×3×10=204×10=2040
3. Combined sum =1440+2040=3480.
4. Total students =20+30=50.
5. Combined average =3480÷50 Do division: 3480÷50=(3480÷10)÷5=348÷5=69.6

Answer : 69.6

8. Average after adding or removing numbers

(a) Removing a number

Example: Average of 8 numbers is 15. One number 10 is removed. New average?

1. Original total =15×8=120
2. After removing 10: new total =120−10=110.
3. New count =7
4. New average =110÷7 Long division: 7×15=105 remainder 5 → 15×5/7=15.714285….

Answer: 110/7 = 15.714…

(b) Adding a number (find the added number)

Rule: If original avg =A for n numbers and new avg =B after adding one number, the added number x=B(n+1)−An.

Example: Average of 4 numbers is 12. After adding one number the new average becomes 13. Find the new number.

1. Original total =12×4=48
2. New total =13×5=65
3. Added number =65−48=17

Answer: 17

9) Weighted average (different weights)

Idea: Multiply each value by its weight, add, then divide by total weights.

Example: Marks — Maths 80 (weight 3), Science 70 (weight 2), English 60 (weight 1). Find weighted average.

Step-by-step:

1. Weighted sum =80×3+70×2+60×1.
   • 80×3=240
   • 70×2=140
   • 60×1=60
   • Sum =240+140+60=440.
2. Total weights =3+2+1=6
3. Weighted average =440÷6=73.333…

Answer: 73.33

10) Average speed problems (special — do not use plain mean)

Two common cases:

(A) Equal distances at different speeds — use the harmonic mean:

Avg speed=v1​1​+v2​1​2​

Avg speed= 2 / 1/v1+1/v2

Example: 120 km at 60 km/h and return 120 km at 40 km/h (equal distances).

1. For equal distances the harmonic mean formula simplifies: 2/(1/60+1/40)
2. Compute 1/60=0.016666…,  1/40=0.025. Sum =0.041666…
3. 2÷0.041666…=48 km/h.

Answer: 48 km/h

(B) Equal time spent at different speeds — arithmetic mean applies:
If you drive 1 hour at 50 km/h and 1 hour at 70 km/h, average speed =(50+70)/2=60=(50+70)/2=60=(50+70)/2=60 km/h.

Key: Equal distance → harmonic mean. Equal time → arithmetic mean.

11) Problems where group size is unknown (solve equation)

Example: Group A: 30 people average 75. Group B average 60. Combined average is 70. Find size of Group B.

Set up:

75×30+60×y/30+y = 70

Compute stepwise

1. 75×30=2250
2. Equation: (2250+60y)=70(30+y)=2100+70y
3. Move terms: 2250−2100=70y−60y⇒150=10y
4. So y=15

Answer: 15 people in Group B.

Quick summary of formulas / tricks

• Sum = average × count.
• Missing number = total required − sum of known.
• Combined average =A1n1+A2n2/n1+n2
• New number when average changes x=B(n+1)−An
• If one number increased by k: new average =old total+k/n
• Weighted average =∑wixi/∑wi
• Average speed (equal distances) =2/1/v1+1/v2
• For equal times, average speed = arithmetic mean.

Practice – Maths-1 Average

1. Average of 6 numbers is 25. Five numbers: 20, 25, 30, 24, 26. Find the 6th.
2. Two groups: 15 people avg 72, 10 people avg 68 → combined avg?
3. Average of 9 numbers is 40. A new number 70 is added. New average?
4. Average of 5 numbers is 48. One number 60 is removed. New average?
5. Travel 120 km at 60 km/h and 120 km at 40 km/h. Avg speed?
6. Marks: 85 (weight2), 75 (weight3), 90 (weight5). Weighted average?
7. Average of 20 students is 70. 5 new students with average 60 join. New average?

Answers – Maths-1 Average

1. 16.
2. 69.6.
3. 43
4.  45
5.  48km/h
6.  84.5

7. New total initial = 20×70=1400

added total 5×60=300

combined total =1700; count =25new avg =1700/25=68