Question

In a village
the number of houses and the number of flats of are in the ratio 9:5
The number of flats and the number of bungalows in the ratio 10:3
There are 30 bungalows in the village
How many houses are there in the village?

Answer 1

A n s w e r

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G i v e n

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• Number of houses and the number of flats of are in the ratio 9:5

• Number of flats and the number of bungalows in the ratio 10:3

• There are 30 bungalows in the village

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F i n d

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• Number of houses in the village

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S o l u t i o n

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Given that , number of houses and the number of flats of are in the ratio 9:5

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So,

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• Let the number of houses be "9x"

• Let the number of flats be "5x"

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$\underline{\bold{\texttt{Number of houses :}}}$

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➠ 9x ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{Number of flats :}}}$

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➠ 5x ⚊⚊⚊⚊ ⓶

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Also given that , number of flats and the number of bungalows in the ratio 10:3

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So,

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• Let the number of flats be "10y"

• Let the number of bungalows be "3y"

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$\underline{\bold{\texttt{Number of flats :}}}$

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➠ 10y ⚊⚊⚊⚊ ⓷

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$\underline{\bold{\texttt{Number of bungalows :}}}$

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➠ 3y ⚊⚊⚊⚊ ⓸

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It is given that the total number of bungalows are 30

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So ,

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From ⓸

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➜ 3y = 30

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➜ $\sf y = \dfrac { 30 } { 3 }$

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➜ y = 10 ⚊⚊⚊⚊ ⓹

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⟮ Putting y = 10 from ⓹ to ⓷ ⟯

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➜ 10y

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➜ 10(10)

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➨ 100 ⚊⚊⚊⚊ ⓺

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• Hence the number of flats is 100

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From ⓶ we get the number of flats is 5x

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So ,

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➜ 5x = 100

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➜ $\sf x = \dfrac { 100 } { 5 }$

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➜ x = 20 ⚊⚊⚊⚊ ⓻

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⟮ Putting x = 20 from ⓻ to ⓵ ⟯

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➜ 9x

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➜ 9(20)

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➨ 180

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• Hence there are 180 houses in the village