Two students appeared for an examination. One of them secured $19$ marks more than the other and his marks were $60 \%$ of the sum of their marks. The marks obtained by them are

If the numerator of a fraction is increased by $150 \%$ and the denominator of the fraction is increased by $350 \%,$ the resultant fraction is $\frac{25}{51},$ what is the original fraction?

The value of a machine depreciates at the rate of $10 \%$ every year. It was purchased $3$ years ago. If its present value is $₹ 8748$,its purchase price was:

The population of a town is $9000$. If the number of females increases by $5 \%$ and the males by $7.5 \%$,what will be the total population after the increase? The number of females currently is $3000$.

The price of onions has been increased by $50 \%$. In order to keep the expenditure on onions the same,the percentage of reduction in consumption has to be:

An index of $12$ shares contains,among others,the shares of Vision Power,Vision Infra,and Vision Communication with weightage of $7\%$,$13\%$,and $15\%$ respectively. What is the increase in the prices of other shares,if these three rise by $9\%$,$10\%$,and $4\%$ respectively,while the index rises by $6\%$?