Question

A family of 8 people have enough food for 30 days. Due to some guests, the food was consumed in 20 days. How many guests joined the family??​

Answer 1

Answer:

Let the number of guests who joined be 'x'.

It is given that a particular amount of food was sufficient for 8 members for 30 days. When 'x' members were added, the number of days . reduced to 20. Hence we are required to the number of members who joined.

This is a question based on Inverse Proportion. (Reason: It's because one quantity varies inversely with the other. That is, if one quantity increases, other decreases.)

Hence if x : y :: a : b, then according to inverse proportion rule,

⇒ x × y = a × b

Now converting the given data in terms of inverse proportion, we get:

⇒ 8 members : 30 days :: ( 8 + x ) members : 20 days

Applying the formula we get:

⇒ 8 × 30 = ( 8 + x ) × 20

⇒ 240 = 160 + 20x

⇒ 240 - 160 = 20x

⇒ 80 = 20x

⇒ x = 80/20

⇒ x = 4

Hence the number of guests who joined the family is 4.

Answer 2

Answer:

Given :-

• A family of 8 people have enough food for 30 days. Due to some guests, the food was consumed in 20 days.

To Find :-

• How many guests joined the family.

Solution :-

Let, the number of guests joined the family be x

According to the question,

⇒ $\sf 20 \times (x + 8) =\: 8 \times 30$

⇒ $\sf 20x + 160 =\: 240$

⇒ $\sf 20x = 240 - 160$

⇒ $\sf 20x =\: 80$

⇒ $\sf x =\: \dfrac{\cancel{80}}{\cancel{20}}$

➠ $\sf\bold{\red{x =\: 4}}$

$\therefore$ The number of guests joined the family is 4 .

${\purple{\boxed{\large{\bold{VERIFICATION :-}}}}}$

↦ $\sf 20 \times (x + 8) =\: 8 \times 30$

↦ $\sf 20x + 160 =\: 240$

By putting x = 4 we get,

↦ $\sf 20(4) + 160 = 240$

↦ $\sf 80 + 160 =\: 240$

↦ $\sf 240 =\: 240$

➦ LHS = RHS

Hence, Verified ✔