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Sum Natural Numbers Subset

This Question is for Sum Natural Numbers Subset. Natural Numbers have been subgrouped into different subsets and it is required to find the sum of the elements in the subset 50.

Sum Natural Numbers of the Subset 50

(Q.) N the set of natural numbers is partitioned into subsets {S}_{1}=(1) , {S}_{2}=(2,3) ,{S}_{3}=(4,5,6) ,{S}_{4}=(7,8,9,10) and so on. The sum of the elements of the subset {S}_{50} is
CAT 1990 Question

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Integral Numbers Satisfying Given Condition

This Question is for finding Integral Numbers Satisfying the given Condition where the product of digits of the Number equals their Sum.

(Q.)For a positive integer n, let {P}_{n} denote the product of the digits of n and {S}_{n} denote the sum of the digits of n. The number of integers between 10 and 1000 for which {P}_{n} + {S}_{n} =n is:

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