Aditya and Manish continued in a joint business for $36$ months. Aditya contributed $Rs. 300$ for a certain time and Manish invested $Rs. 500$ for the remaining time. If out of a total profit of $Rs. 1020$,Aditya gets $Rs. 495$,then for how many months did Aditya keep his money?

Two casks of $48$ $litres$ and $42$ $litres$ are filled with mixtures of wine and water,the proportions in the two casks being respectively $13:7$ and $18:17$. If the contents of the two casks are mixed,and $20$ $litres$ of water is added to the whole,what will be the proportion of wine to water in the resultant mixture?

$A$ man buys $2$ cows for $Rs. 2700$ and sells one at a loss of $6\%$ and the other at a gain of $7.5\%$. On the whole,he neither gained nor lost. What is the cost price of the $2^{nd}$ cow?

In a mixture of $60\, L$,the ratio of acid and water is $2:1$. If the ratio of acid and water is to be $1:2$,then the amount of water (in $litres$) to be added to the mixture is:

$A$ mixture of $80$ litre of milk and water contains $10 \%$ water. How much water must be added to make $20 \%$ water in the new mixture? (in $litre$)

In a mixture of $25\, L$,the ratio of acid to water is $4: 1$. Another $3\, L$ of water is added to the mixture. The ratio of acid to water in the new mixture is