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Ten trucks, numbered $1$ to $10$ , are carrying packets of sugar. Each packet weights either $999\,g$ or $1000\,g$ and each truck carries only the packets equal weights. The combined weight of $1$ packet selected from the first truck,$2$ packets from the second,$4$ packets from the third, and so on, and $2^9$ packet from the tenth truck is $1022870\,g$. The trucks that have the lighter bags are
$1,3,5$
$2,4,5$
$1,9$
$2,8$
Solution
(d)
If all trucks had packets of $1000\,g$, then total weight is
$1000(1+2 \left.+2^2+\ldots+2^9\right)$
$=1000\left(2^{10}-1\right)$
$=1000(1024-1)=1023000$
We have given total weight is $1022870$.
$\therefore 1022870 < 1023000$
Extra amount of weight
$=1023000-1022870$
$=130$
$130 =2^7+2^1=128+2$
$\therefore$ The trucks have the lighter bags are $2,8$
