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Let 'x' be the total weight of 100 screws in box 'A'

therefore,

average weight of 100 screws in box 'A' = (x / 100) = 10.4

=> x = 100*10.4 = 1040 gms ............ (1)

Let 'y' be the total weight of 150 screws in box 'B',

therefore,

average weight of 150 screws in box 'B' = (y / 150) .......... (2)

After mixing 100 screws of 'A' and 150 screws of 'B',

average weight of 250 screws = (x+y)/250 = 10.9

=> x+y = 250*10.9 = 2725

=> 1040+y = 2725

=> y = 2725 - 1040 = 1685

=> total weight of 150 screws of box 'B', y = 1685 gms

Substitute y = 1685 in eqn (2),

=> average weight of screws of box 'B' = 1685/150 = 11.23 gms (approx)

Hence,

average weight of screws of box 'B' = 11.23 gms

SHORT ANSWER

"""""""""""""""""

Given data:

No. of screws in box 'A', NA = 100

No. of screws in box 'B', NB = 150

Average weight of 100 screws in box 'A', XA = 10.4 gms

Average weight of mixed screws, XAB = 10.9 gms

Average weight of 150 screws in box 'B', XB = ?

Therefore,

XAB = (NA XA + NB XB) / (NA + NB)

10.9 = (100*10.4 + 150XB) / (100+150)

10.9 = (1040 + 150XB) / 250

10.9*250 = 1040 + 150XB

2725 = 1040 + 150XB

2725 - 1040 = 150XB

1685 = 150XB

XB = 1685/150 = 11.23 gms

XB = 11.23 gms

- Ratnakar Sharma

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Q: Average weight of 100 screws in box 'A' is 10.4gms it is mixed withed with150 screws of box 'B' average weight of mixed screws is 10.9 gms find the average weight of screws of box 'B'?
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