There are 40 boys in a class A and 60 girls in class B. If girls in class A are `80%` of girls in class B. total students in class B are `50%` more than total students in class A. find number of boys in class B. (total students = no. of boys + no. of girls)

Options

A. 72
B. 75
C. 80
D. 62

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
- Class A has 40 boys.
- Class B has 60 girls.
- Girls in class A are 80% of girls in class B.

### Step 2: Calculate the number of girls in class A
Let the number of girls in class B be denoted as G_B. According to the problem, girls in class A (G_A) are 80% of girls in class B.

\[ G_A = 0.8 \times G_B \]

Since we know that G_B = 60 (the number of girls in class B):

\[ G_A = 0.8 \times 60 = 48 \]

### Step 3: Calculate the total number of students in class A
The total number of students in class A (T_A) is the sum of boys and girls in class A:

\[ T_A = \text{Number of boys in A} + \text{Number of girls in A} \]
\[ T_A = 40 + 48 = 88 \]

### Step 4: Determine the total number of students in class B
According to the problem, the total number of students in class B (T_B) is 50% more than the total number of students in class A.

To find 50% more than T_A:

\[ T_B = T_A + 0.5 \times T_A \]
\[ T_B = 88 + 0.5 \times 88 = 88 + 44 = 132 \]

### Step 5: Calculate the number of boys in class B
Now, we know the total number of students in class B (T_B) is 132, and we already know that there are 60 girls in class B.

To find the number of boys in class B (B_B):

\[ B_B = T_B - \text{Number of girls in B} \]
\[ B_B = 132 - 60 = 72 \]

### Conclusion
The number of boys in class B is **72**.

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