Question : Divide INR 1488 among X, Y, and Z. If the shares are in the ratio X : Y = 4 : 5 and Y : Z = 7 : 6, then find out the share of Z.
Option 1: INR 460
Option 2: INR 450
Option 3: INR 470
Option 4: INR 480
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Correct Answer: INR 480
Solution :
INR 1488 is divided among X, Y, and Z.
⇒ X + Y + Z = 1488 .......(1)
Given, X : Y = 4 : 5 and Y : Z = 7 : 6
⇒ X = $\frac{4}{5}$Y and Y = $\frac{7}{6}$Z
⇒ X = $\frac{4}{5}\times \frac{7}{6}$Z = $\frac{14}{15}$Z
Putting in (1), we get,
$\frac{14}{15}$Z + $\frac{7}{6}$Z + Z = 1488
⇒ $\frac{1}{30}$(28Z + 35Z + 30Z) = 1488
⇒ 93Z = 44640
⇒ Z = 480
Hence, the correct answer is INR 480.
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