$\frac{1}{4}$ of the passengers of a train are children, $\frac{2}{5}$ of the passengers are males and the rest are females. If the the number of females travelling in the train is $420$ , find the total number of passengers in the train.

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Solution

Let total number of passenger in train $= x$
Total number of children passengers $= \frac{1}{4} x$
Total number of male passenger $= \frac{2}{5} x$
Remaining passengers which are females $= 420$
$x - (\frac{x}{4} + \frac{2 x}{5}) = 420 \Rightarrow x - (\frac{5 x + 8 x}{20}) = 420 \Rightarrow x - \frac{13 x}{20} = 420 = \frac{20 x - 13 x}{20} \Rightarrow \frac{7 x}{20} = 420 x = \frac{420 \times 20}{7} x = 1200$
Hence, total number of passengers $= 1200$ .

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14 of the passengers of a train are children, 25 of the passengers are males and the rest are females. If the the number of females travelling in the train is420, find the total number of passengers in the train.

Let total number of passenger in train =xTotal number of children passengers =14xTotal number of male passenger =25xRemaining passengers which are females =420 x-x4+2x5=420⇒x-5x+8x20=420⇒x-13x20=420=20x-13x20⇒7x20=420x=420×207x=1200Hence, total number of passengers =1200.

$\frac{1}{4}$ of the passengers of a train are children, $\frac{2}{5}$ of the passengers are males and the rest are females. If the the number of females travelling in the train is $420$ , find the total number of passengers in the train.