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
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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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