If $432P1$ is completely divisible by $9$,then what is the value of $P$?

The unit digit in the product $(2467)^{153} \times (341)^{72}$ is

$6 \frac{1}{15}-4 \frac{1}{12}+7 \frac{1}{3}-2 \frac{1}{6}=?$

Find the least number which when divided by $12, 18, 36$ and $45$ leaves the remainder $8, 14, 32$ and $41$ respectively.

The price of commodity $X$ increases by $40 \text{ paise}$ every year,while the price of commodity $Y$ increases by $15 \text{ paise}$ every year. If in $2001$,the price of commodity $X$ was $Rs. 4.20$ and that of $Y$ was $Rs. 6.30$,in which year will commodity $X$ cost $40 \text{ paise}$ more than commodity $Y$?

Three numbers are in the ratio $4: 5: 6$ and their average is $25$. The largest number is