Question

one evening kaya devoted 2/5 of her study time to mathematics, 3/20 of her time to social science ,1/3 of her time to chemistry and the remaining 42 minutes to English. how much did she spend studying social science?​

Answer 1

$\bf{Let \ the \ time \ devoted \ by \ Kaya \ in \ her}$

$\bf{studies \ be \ x \ minutes}$

$\bf{:\longmapsto{Time \ devoted \ in \ studying \ maths = \dfrac{2x}{5}}}$

$\bf{:\longmapsto{Time \ devoted \ in \ studying \ SSt = \dfrac{3x}{20}}}$

$\bf{:\longmapsto{Time \ devoted \ in \ studying \ Chemistry = \dfrac{x}{3}}}$

$\bf{:\longmapsto{Time \ devoted \ in \ studying \ English = 42 \ min}}$

$\bf{Total \ time \ devoted \ by \ Kaya \ in \ her \ studies \ (x)}$

$\bf{= \dfrac{2x}{5} + \dfrac{3x}{20} + \dfrac{x}{3} + 42}$

⇒ $\bf{x = \dfrac{2x}{5} + \dfrac{3x}{20} + \dfrac{x}{3} + 42}$

⇒ $\bf{x - \dfrac{2x}{5} - \dfrac{3x}{20} - \dfrac{x}{3} = 43}$

⇒ $\bf{\dfrac{60x - 24x - 9x - 20x}{60} = 42}$

⇒ $\bf{7x = 42 × 60}$

⇒ $\bf{x = \dfrac{2520}{7}}$

⇒ $\fbox{\bf{x = 360}}$

$\red{\bf{So \ time \ devoted \ in \ studying \ SSt}}$

$\red{\bf{= \dfrac{3x}{20} = \dfrac{3}{20} × 360 = 54 \ min}}$

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