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Narayanganj Higher Secondary 2014 P5

Posted: Mon Feb 18, 2019 7:54 pm
by samiul_samin
Every participants of a picnic are given a lottery coupon. The coupons are numbered from $1$ and consequently. The winner’s coupon number, and the all coupons number are added and the sum is $2610$. What is the number of coupon which was winner?

Re: Narayanganj Higher Secondary 2014 P5

Posted: Thu Oct 31, 2019 8:46 pm
by Ragib Farhat Hasan
$1+...+10=55$
$11+...+20=100+55$
$21+...+30=200+55$
$31+...+40=300+55$
$41+...+50=400+55$
$51+...+60=500+55$
$61+...+70=600+55$

Adding=> $100(1+...+6)+55\times7=2485$

Now, $2610-2485=125$, which is not possible.

Adding $71$ to $2485$, the summation of all the coupon numbers become $2556$.

Therefore, the winning coupon number is $54$.