Question

# Study the pattern and solve it by giving an explanation.$4812=14,62430=6,278=?$.

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Solution

## We have to study the pattern first and then solve the last part based on that pattern.In the first case, $4812=14$ The sum of all numbers written in $\mathrm{L}.\mathrm{H}.\mathrm{S}=4+8+12=24$Now, we observe that, $\mathrm{R}.\mathrm{H}.\mathrm{S}\left(14\right)=2×4+2+4$$⇒\mathrm{R}.\mathrm{H}.\mathrm{S}=$ product of digits $+$sum of digits.Similarly on the same pattern in the second case, $62430=6$The sum of numbers, $6+24+30=60$Now, in $60$, the sum of digits $+$product of digits $=6+0+6×0=6$So, by using same pattern, in the third case $278=?$ , we haveSum of numbers $=2+7+8=17$Now, sum of digits $+$ product of digits $=1+7+1×7=15$.Hence, the required answer is $15$.

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