a pack contains n cards numbered 1 to n .Two consecutive cards are removed from the pack and sum of remaining card is $1224$ .If smaller of number on the removed card is k.Find value of $k - 20$

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Solution

Given

$\frac{n (n + 1)}{2} - (k) - (k + 1) = 1224$

get $k = n (n + 1) - \frac{2450}{4}$

since n should be such that

$n (n + 1) > 2450$ and

k is integer only $n = 50$ satisfies , then

$k = 25$ and

$k - 20 = 5$

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a pack contains n cards numbered 1 to n .Two consecutive cards are removed from the pack and sum of remaining card is 1224.If smaller of number on the removed card is k.Find value of k−20

Given n(n+1)2−(k)−(k+1)=1224 get k=n(n+1)−24504 since n should be such that n(n+1)>2450 and k is integer only n=50 satisfies , then k=25 and k−20=5

a pack contains n cards numbered 1 to n .Two consecutive cards are removed from the pack and sum of remaining card is $1224$ .If smaller of number on the removed card is k.Find value of $k - 20$

Given

$\frac{n (n + 1)}{2} - (k) - (k + 1) = 1224$

get $k = n (n + 1) - \frac{2450}{4}$

since n should be such that

$n (n + 1) > 2450$ and

k is integer only $n = 50$ satisfies , then

$k = 25$ and

$k - 20 = 5$