Math, asked by AkritiaBianoi, 5 months ago

The sum of 6 consecutive numbers is 105. Find the smallest number.

A 13

B 15

C 14

D 12​

Answers

Answered by Anonymous
6

Given:

  • The sum of 6 consecutive numbers is 105.

To find:

  • The smallest number  ?

⠀⠀⠀⠀⠀⠀⠀

Solution:

Let the six consecutive numbers x, x + 1, x +2, x + 3, x + 4, x + 5.

➜ x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 105

➜ 6x + 15 = 105

➜ 6x = 105 - 15

➜ 6x = 90

x = 15

Therefore, option (b) is correct.

⠀⠀⠀━━━━━━━━━━━━━━━━━⠀⠀

Answered by ILLUSTRIOUS27
2

Given

  • The sum of 6 consecutive numbers is 105.

To Find

  • the smallest number.

Solution

We have given that the sum of consecutive numbers (e.g. 2,3,4,5) is 105 we need to find the smallest number (in example 2)

We need to let the smallest number be x

Therefore,

  • Number1=x
  • Number2=x+1
  • Number3=x+2
  • Number4=x+3
  • Number5=x+4
  • Number6=x+5
  • Sum of numbers=105

Adding all numbers we get

 \rm \: x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 \\  \\  \implies \rm \: 6x + 15

Now write the equation which is given

ATQ

 \rm \: 6x + 15 = 105 \\  \\  \implies \rm \: 6x = 105 - 15 \\  \\  \implies \rm \: 6x = 90  \\   \\   \implies \boxed{ \bf \: x = 15}

Hence the smallest number is x i.e. 15

And all numbers are

  • Number1=15
  • Number2=16
  • Number3=17
  • Number4=18
  • Number5=19
  • Number6=20

Hence the answer is (b).

Similar questions