Chapter 8, Problem 31RP

To determine

To calculate:The second number using the given condition.

Answer to Problem 31RP

The second number is 75

Explanation of Solution

Given information:

The sum of four numbers is 771

The ratio of first to second is 2:3

The ratio of second to third is 5:4

The ratio of third to fourth is 5:6

Formula used:

From the ratios, find the value of all the numbers in term of second numbers and take out from second number from the equation formed for the sum of numbers

Calculation :

Let the numbers be x, y, z and w.

Given,

  $\begin{array}{l}x+y+z+w=\mathrm{771.....}\left(i\right)\\ \frac{x}{y}=\frac{2}{3}\Rightarrow x=\frac{2}{3}y\mathrm{......}\left(ii\right)\\ \frac{y}{z}=\frac{5}{4}\Rightarrow z=\frac{4}{5}y\mathrm{......}\left(ii\right)\\ \frac{z}{w}=\frac{5}{6}\Rightarrow w=\frac{6}{5}z=\frac{6}{5}\times \frac{4}{5}y=\frac{24}{25}y\mathrm{......}\left(iii\right)\end{array}$

Now, on putting the values of x, z and w in eq (i), we get

  $\begin{array}{l}\frac{2}{3}y+y+\frac{4}{5}y+\frac{24}{25}y=771\\ \Rightarrow 50y+75y+60y+72y=771\times 25\\ \Rightarrow 257y=771\times 25\\ \Rightarrow y=3\times 25=75\end{array}$