Question

The sum of 3 consecutive numbers of the four numbers a, b, c, d are 4613,4961,5010,5099 then what is the largest number among a,b,c,d ?

Answer 1

Question ask for sum of three numbers out of given four numbers a,b,c,d

we can make total four sets of any 3 numbers taken at a time

those sets are : a,b,c

a,c,d

a,b,d

b,c,d

apart from these four sets no more collection of 3 numbers out of given four numbers can be made .

let us start writing the sum of these numbers

Let us suppose sum of a+b + c = 4613 --------------eqn (1)

a+ c + d = 4961----------- eqn (2)

a+b+ d = 5010 ------------ eqn ( 3)

b+ c + d = 5099 --------eqn ( 4)

Let us add all four equations : 3a+ 3b + 3c+ 3d = 19683

3( a+b+c+d) = 19683

a+b+c+d = 6561 --------eqn ( 5)

Let us start subtracting all eqn (1) to (4) from eqn ( 5)

eqn ( 5) - eqn ( 1) = d= 1948

eqn ( 5) - eqn ( 2) = b= 1600

eqn ( 5) - eqn ( 3) c= 1551

eqn ( 5) - eqn (4) a = 1462

We can see that d is the largest number that is 1948