Question

The ratio of the number of letters delivered to Post Office A to that delivered to Post Office B to that delivered to Post Office C is 3:5: 4. If Post Office C received 72 letters, how many letters did Post Office B receive? What is the total number of letters delivered to all the three post offices?​

Answer 1

The number of letters received by Post Office B is equal to 90 and the total number of letters delivered to all three post offices is equal to 216.

Given:

The ratio of the number of letters delivered to Post Office A, Post Office B and Post Office C is equal to 3 : 5 : 4.

Post Office C received 72 letters.

To Find:

The number of letters received by Post Office B and the total number of letters delivered to all three post offices.

Solution:

→ The ratio of the number of letters delivered to Post Office A, Post Office B and Post Office C is equal to 3 : 5 : 4.

→ Let the number of letters delivered to Post Office A be 3x.

 ∴ The number of letters delivered to Post Office B = 5x

 ∴ The number of letters delivered to Post Office C = 4x

→ Since Post Office C received 72 letters.

                            ∴ 4x = 72

                            ∴ x = 72/4

                            ∴ x = 18

→ The value of 'x' comes out to be equal to 18.

  ∴ The number of letters delivered to Post Office A = 3x = 3(18) = 54

  ∴ The number of letters delivered to Post Office B = 5x = 5(18) = 90

→ Calculating the total number of letters delivered to all post offices:

 ∴ The total number of letters delivered to all post offices = 54 + 90 + 72

 ∴ The total number of letters delivered to all post offices = 216

The number of letters received by Post Office B is equal to 90 and the total number of letters delivered to all three post offices is equal to 216.

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Answer 2

Answer: Post office B received 90 letters and all the three post received total of 216 letters.

Given: Ratio of letters received by all are 3:5:4. and C received 72 letters.

To Find: Number of letters post office B received and total number of letters delivered to all three post offices.

Step-by-step explanation:

Step 1: Let Post office A delivered 3x letters, post office B delivers 5x letters and post office C delivers 4x letters.

Since Post office C received 72 letters i.e.

$4x=72\implies x=18$

So, number of letters post office B received = $5x=5\times 18=90$

Post office B received 90 letters.

Step 2: Total number of letters delivered to all the three post offices = $3x+5x+4x$

$=12x\\=12\times 18\\=216$

Total number of letters received by all the post offices is 216.

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