Question

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

Answer 1

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.

Answer 2

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.

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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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