Practice Exercises

Between two stations Kanpur and Mumbai the first, second and third class fares were fixed in the ratio of $8: 6: 3$. However, when Mr L Prasad, the railway minister, presented the railway budget, he reduced the first class fares by $\frac{1}{6}$ and the second class by $\frac{1}{12}$ in order to rationalize the fares vis-à-vis the second-class fares. In a year, ratio of the number of first, second and third class passengers were, respectively, $9: 12: 26$ and the money at the booking offices was ₹$1,08,800$. How much was paid by the first class passengers?

If $29$goats can feed on a field of uniformly grown grass in $7$days or $25$goats can feed on the same field in$9$ days, how many goats will feed in 6 days?

Given, $\mathrm{x}: \mathrm{y}=\mathrm{a}: \mathrm{b}=1: 5$. Then, the value of $\frac{{\mathrm{x}}^2+{\mathrm{a}}^2}{{\mathrm{y}}^2+{\mathrm{b}}^2}?$

$\mathrm{a}, \mathrm{b}$, and $\mathrm{c}$ are three positive numbers and  $\mathrm{s}=\frac{(\mathrm{a}+\mathrm{b}+\mathrm{c})}{2}$. If $(\mathrm{s}-\mathrm{a}):(\mathrm{s}-\mathrm{b}):(\mathrm{s}-\mathrm{c})=1: 7: 4$, the ratio of $\mathrm{a}: \mathrm{b}: \mathrm{c}$ ?

In an election, each voter may vote for two candidates. Half of the voters vote for $\mathrm{A}$, but divide their votes between $\mathrm{B}, \mathrm{C}$, and $\mathrm{D}$ in the ratio of  $3: 2: 1$. Of the remaining, half vote for $\mathrm{B}$ and divides their votes between $\mathrm{C}$ and $\mathrm{D}$ in the ratio of  $2: 1$. Of the remaining, half vote for $\mathrm{C}$ and $\mathrm{D}$ and the remaining $840$do not vote for anyone. How many votes were received by $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$, respectively?

The square of the time taken by a planet to complete one revolution around the sun varies as the cube of its mean distance from the sun. If the ratio of the mean distances of Mars and Saturn from the sun is $16:3$. Find the number of days on Saturn that are equal to a year on Mars.

In a forest reserve, the ratio of the number of deers, bear and fox is $3: 7: 5$. If the difference between the number of deers and bears is a multiple of $3$ as well as  $7$ , what is the minimum number of animals in the park?

Shalaj and Associates, a shoe-manufacturing company, has three machines producing shoes. If machine $\mathrm{X}$ produces $\frac{1}{4}$ th as many as machine $\mathrm{Y}$ produces in the same time, and machine $\mathrm{Y}$ produces twice as many as machine $\mathrm{Z}$ produces in the same time, then during a fixed time, what fraction of the total number of shoes is produced by machine $\mathrm{Z}$?