# The sum of the ages of five students is as follows: Ada and Bob is 39, Bob and Chim is 40, Chim and Dan is 38, Dan and Eze is 44. The total sum of all the five ages is 105. Questions What is the age of the youngest student? Who is the oldest student?

Jun 13, 2018

Age of youngest student , Dan is $16$ years and Eze is the oldest student of $28$ years age.

#### Explanation:

Sum of ages of Ada,Bob, Chim, Dan and Eze :$105$ years

Sum of ages of Ada & Bob is $39$years.

Sum of ages of Bob & Chim is $40$years.

Sum of ages of Chim & Dan is $38$years.

Sum of ages of Dan & eze is $44$years. Therefore,

Sum of ages of Ada,Bob (2), Chim (2), Dan(2) and Eze is

$39 + 40 + 38 + 44 = 161 y e a r s$ Therefore,

Sum of ages of Bob, Chim , Dan is $161 - 105 = 56$ years

Therefore age of Dan is $56 - 40 = 16$ years , age of Chim is

$38 - 16 = 22$ years , age of Eze is $44 - 16 = 28$, age of

Bob is $40 - 22 = 18$ years and age of Ada is $39 - 18 = 21$ years

Ages of Ada,Bob, Chim, Dan and Eze are $21 , 18 , 22 , 16 \mathmr{and} 28$

years respectively.Age of youngest student , Dan is $16$ years

and Eze is the oldest student of $28$ years age. [Ans]

Jun 13, 2018

$\to$Age of the youngest student is 16 years ( Dan )

$\to$The oldest student is Eze ( 28 years )

#### Explanation:

Let the age of Ada, Bob, Chim, Dan and Eze be $A , B , C , D \mathmr{and} E$respectively.

Now, as per the question :

$A + B = 39$ ... (i)

$B + C = 40$ ... (ii)

$C + D = 38$ ... (iii)

$D + E = 44$ ... (iv) and

$A + B + C + D + E = 105$

$\therefore \left(A + B\right) + C + \left(D + E\right) = 105$

$\therefore 39 + C + 44 = 105$ ... [Substituting the value of $A + B \mathmr{and} D + E$ from (i) and (iv)]

$\therefore C + 83 = 105$

$\therefore C + 83 - 83 = 105 - 83$

$\therefore C = 22$ ... (v)

Now, in equation (ii) and (iii),

$B + C = 40 \mathmr{and} C + D = 38$

$\therefore B + 22 = 40 \mathmr{and} 22 + D = 38$ ... [Substituting the value of $C$ from (v)]

$\therefore B = 18 \mathmr{and} D = 16$

Now, in equation (i) and (iv),

$A + B = 39 \mathmr{and} D + E = 44$

$\therefore A + 18 = 39 \mathmr{and} 16 + E = 44$ ... [Substituting the value of $B$ and $D$]

$\therefore A = 21 \mathmr{and} E = 28$

Hence,

Age of Ada : $21$

Age of Bob : $18$

Age of Chim : $22$

Age of Dan : $16$

Age of Eze : $28$

Therefore, the age of the youngest student is 16 years (Dan) and the oldest student is Eze (28 years).