Question

3. There are four numbers. Average of the first three
is 15 and of last three is 16. If the last number is
19, find the first number.
(a) 16
(6) 20
(c) 19
(d) None of these
please solve this question​

Answer 1

Answer:

( a )

Step-by-step explanation:

Let the numbers are a, b, c and d.

Given,

        Average of first three numbers is 15.

It means : average of a , b and c is 15.

   ⇒ ( a + b + c ) / 3 = 15

   ⇒ a + b + c = 15 x 3

  ⇒ a + b + c = 45            ...( 1 )

Also,

       Average of last three numbers is 16.

     ⇒ ( b + c + d ) / 3 = 16

     ⇒ b + c + d = 16 x 3

     ⇒ b + c + d = 48          ...( 2 )

Subtracting ( 2 ) from ( 1 ) :

⇒ a + b + c - ( b + c + d ) = 45 - 48

⇒ a + b + c - b - c - d = - 3

⇒ a - d = - 3

⇒ a - 19 = - 3           { given d = 19, last number }

⇒ a = 19 - 3

⇒ a = 16

Answer 2

Let the four numbers be,

P, Q, R, S

____________________

Given :-

Average of first 3 numbers = 15

---> P + Q + R/3 = 15

---> P + Q + R = 15 x 3

---> P + Q + R = 45 ...........(1)

Also,

Average of last 3 numbers = 16

---> Q + R + S/3 = 16

---> Q + R + S = 16 x 3

---> Q + R + S = 48 ........(2)

_______________________

It is given that, last number is 19

So,

•°• S = 19

Substituting value of S in (2)

Q + R + S = 48

Q + R + 19 = 48

Q + R = 48 - 19

Q + R = 29 ............(3)

______________________

Substituting (3) in (1),

P + Q + R = 45

P + 29 = 45

P = 45 - 29

P = 16

___________________

•°• Value of (P), first number is 16.