Question

The average weight of A, B, C, D is 60 kg. The

average weight of A, B, C, D, E is 57 kg. The weight

of F is 5 kg more than that of E. The average weight

of B, C, D, E, F is 61 kg. Find the weight of A (in kg).​

Answer 1

Topic :

Average

Given :

Average weight of A, B, C and D is 60 kg.

Average weight of A, B, C, D and E is 57 kg.

The weight of F is 5 kg more than that of E.

Average weight of B, C, D, E and F is 61 kg.

To Find :

Weight of A.

Concept Used :

Average = Sum of terms / Number of terms

Solution :

Average weight of A, B, C and D is 60 kg,

60 kg = ( A + B + C + D ) / 4

4 × 60 kg = A + B + C + D

A + B + C + D = 240 kg

Average weight of A, B, C, D and E is 57 kg,

57 kg = ( A + B + C + D + E ) / 5

5 × 57 kg = A + B + C + D + E

A + B + C + D + E = 285 kg

Calculating weight of 'E',

( A + B + C + D + E ) - ( A + B + C + D ) = 285 kg - 240 kg

A + B + C + D + E - A - B - C - D = 285 kg - 240 kg

E = 285 kg - 240 kg

E = 45 kg

The weight of F is 5 kg more than that of E,

F = E + 5 kg

F = 45 kg + 5 kg

F = 50 kg

Average weight of B, C, D, E and F is 61 kg,

61 kg = ( B + C + D + E + F ) / 5

305 kg = B + C + D + E + F

305 kg = B + C + D + 45 kg + 50 kg

305 kg = B + C + D + 95 kg

305 kg - 95 kg = B + C + D

B + C + D = 210 kg

Calculating weight of 'A',

( A + B + C + D ) - ( B + C + D ) = 240 kg - 210 kg

A + B + C + D - B - C - D = 30 kg

A = 30 kg

Answer :

So, weight of A is 30 kg.

Answer 2

$\huge{ \underline{\boxed{\red{ \color{red}{\textsf {\textbf{An}{\color{blue}{\textbf {\textsf{sw}}{\color{green}{\textbf{\textsf{er}}}{\color{orange}{\textsf{\textbf{~:-}}}}}}}}}}}}}$

$\colorbox{skyblue}{Average weight of A, B, C and Dis 60 kg.}$

➠60 kg (A +B +C+D)/4

➠4x 60 kg = A+B +C+D

➠A+B+C+D 240 kg

$\colorbox{pink}{Average weight of A, B. C. Dand E is 57</p><p>kg.}$

➠57 kg (A +B+C+D+E)/5

➠5 x 57 kg A+B+C +D +E

➠A+B+C+D +E 285 kg

$\colorbox{pink}{Calculating weight of 'E}$

➠(A+B+C+D +E) - (A +B + C+ D) =

285 kg-240 kg

➠A+B+C+D+E - A - B-C-D 285 kg -

240 kg

➠E 285 kg - 240 kg

➠E= 45 kg

$\colorbox{pink}{The weight of F is 5 kg more than that of</p><p>E}$

➠F E+5 kgF 45 kg +5 kg

➠F 50 kg

$\colorbox{pink}{Average weight of B.C. D. E and F is 61</p><p>kg.}$

➠61 kg= ( B+C+D + E+F)/5

➠305 kg =B+C+D+E+F

➠305 kg = B+C+D +45 kg + 50 kg

➠305 kg B+C+D +95 kg

➠305 kg -95 kg = B+C+DB+C+ D= 210 kg

$\colorbox{pink}{Calculating weight of 'A,}$

➠(A+B+C+ D) - ( B+C+D) = 240 kg

210 kg

➠A+B+C+D - B- C- D 30 kg

A 30 kg

$\underline{\underline{\huge{\green{\tt{\textbf Hence, weight \: of \: A \: is \: 30 kg. }}}}}$

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