On Republic Day,sweets were to be equally distributed among $450$ children. But on that particular day,$150$ children remained absent. Thus,each child got $3$ sweets extra. How many sweets did each child get?

$A$ certain amount was to be distributed among $A$,$B$,and $C$ in the ratio $2:3:4$,but was erroneously distributed in the ratio $7:2:5$. As a result of this,$B$ received ₹ $40$ less. What is the actual amount (in ₹)?

The ratio of incomes of $P$ and $Q$ is $3:4$ and the ratio of their expenditures is $2:3$. If both of them save $Rs. 6000$,the total income of $P$ is (in $Rs.$):

When $X$ is subtracted from the numbers $9, 15$ and $27$,the remainders are in continued proportion. What is the value of $X$?

In a school,there were $1554$ students and the ratio of the number of boys to girls was $4:3$. After a few days,$30$ girls joined the school but some boys left; as a result,the ratio of boys to girls became $7:6$. The number of boys who left the school is:

Two candles of the same height are lighted at the same time. The first is consumed in $8 \text{ hours}$ and the second in $6 \text{ hours}$. Assuming that each candle burns at a constant rate,in how many hours after being lighted,the ratio between the height of the first and second candles becomes $2:1$?