Math, asked by Chanchal8474, 9 months ago

A dessert has both fruit and yoghurt inside altogether the mass of the dessert is 185g
the ratio to the mass of fruit to the mass of yoghurt is 2:3
what is the mass of the yoghurt in grams

Answers

Answered by Anonymous
35

The ratio to the mass of Fruit to the mass of Yoghurt is 2:3.

\small{\sf{\:\:\:\:\:\:\:\:\:\:\:\: Assumption}}

Let us assume that the mass of Fruit be 2M and mass of Yoghurt be 3M.

A dessert has both fruit and yoghurt inside altogether the mass of the dessert is 185g.

\small{\sf{\:\:\:\:\:\:\:\:\:\:\:\: As\:per\:given\:condition}}

\implies\:\sf{2M+3M\:=\:185}

\implies\:\sf{5M\:=\:185}

\implies\:\sf{M\:=\:37}

Therefore,

Mass of Fruit = 2M = 2(37) = 74 g

Mass of Yoghurt = 3M = 3(37) = 111 g

\rule{200}2

The ratio to the mass of Fruit to the mass of Yoghurt is 2:3.

\small{\sf{\:\:\:\:\:\:\:\:\:\:\:\: As\:per\:given\:condition}}

\implies\:\sf{\dfrac{Fruit}{Yoghurt}\:=\:\dfrac{2}{3}}

\implies\:\sf{\frac{F}{Y}\:=\:\frac{2}{3}}

\implies\:\sf{F\:=\:\frac{2Y}{3}}

A dessert has both fruit and yoghurt inside altogether the mass of the dessert is 185g.

\small{\sf{\:\:\:\:\:\:\:\:\:\:\:\: As\:per\:given\:condition}}

\implies\:\sf{F+Y\:=\:185}

Substitute value of F above

\implies\:\sf{\frac{2Y}{3}+Y\:=\:185}

\implies\:\sf{\frac{2Y+3Y}{3}\:=\:185}

\implies\:\sf{5Y\:=\:3(185)}

\implies\:\sf{Y\:=\:111}

On solving we get, mass of fruit = 74 g

Therefore,

Mass of Yoghurt is 111g.

Answered by RvChaudharY50
34

Given :-

  • Total Mass = 185g
  • Ratio of Mass of Fruit : Mass of Yoghurt = 2:3.

Solution :-

Lets Assume That, mass of Fruit is 2x g and Mass of yoghurt is 3x g.

So,

Total = 2x + 3x = 185

→ 5x = 185

Dividing both sides by 5,

x = 37.

Hence,

mass of Fruit is 2x = 2*37 = 74 g.

→ Mass of yoghurt is 3x = 3*37 = 111g.

So, Mass of Yoghurt is 111g.

______________________________

Ratio Method :-

Mass of Fruit : Mass of Yoghurt = 2:3.

→ Total = 2 + 3 = 5 unit.

So,

5 unit = 185g.

→ 3 unit = (185/5) * 3 = 111g. (Ans).

_____________________________

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