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Ten trucks numbered 1 to 10 are carrying packets of sugar. Each packet weighs either 999 gms or 1000 gms and each truck carries only the packets of equal weights. The combined weight of 1 packet selected from the first truck, 2 packets from the second truck, 4 packets from the third and so on, upto 2 power 9 packets from the 10th truck is 1022870 gms. The trucks which have the lighter bags are: a) 1.3.5 b)2,4,5 c) 1,9 d)2,8



Ten trucks numbered 1 to 10 are carrying packets of sugar. Each packet weighs either 999 gms or 1000 gms and each truck carries only the packets of equal weights. The combined weight of 1 packet selected from the first truck, 2 packets from the second truck, 4 packets from the third and so on, upto 2 power 9 packets from the 10th truck is 1022870 gms. The trucks which have the lighter bags are:


a) 1.3.5  b)2,4,5  c) 1,9  d)2,8



Grade:12

1 Answers

Manu Pai
31 Points
10 years ago

Calculate 1+2+2^2+.......2^9 which is 1023.

If at all , all the packets are of 1000gms thetotal weights be 1023000.

But the given weight is 1022870gms.

So we replace the difference between them that is 1023000-1022870=130 by replacing 1000 gms packets with 999gm packets.

So just see the option on whose replacement gives a difference of 1130.

That is option no. (d)2,8.

becoz 2(1000)+2^7(1000)-2(999)-2^7(999)=130

1023000-2(1000)+2^7(1000)-2(999)-2^7(999)=1023000-130=1022870.

 

MANULaughing

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