Last year,there were 610 boys in a school.Then umber decreased by 20% this year.How many girls are there in the school, if the number of girls is 175% of the total number of boys in the school this year?

Options

A. 854
B. 848
C. 798
D. 782

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Calculate the number of boys this year after a 20% decrease.

1. **Initial number of boys last year**: 610
2. **Percentage decrease**: 20%

To find the number of boys this year, we calculate the remaining percentage of boys after the decrease:
- Remaining percentage = 100% - 20% = 80%
- In decimal form, this is 0.80.

Now, we can calculate the number of boys this year:
\[ \text{Number of boys this year} = 610 \times 0.80 \]

### Step 2: Perform the multiplication.

Calculating:
\[ 610 \times 0.80 = 488 \]

So, the number of boys this year is **488**.

### Step 3: Calculate the number of girls based on the number of boys.

We know that the number of girls is 175% of the number of boys this year.

1. **Percentage of girls**: 175%
2. **In decimal form**: 175% = 1.75

Now we calculate the number of girls:
\[ \text{Number of girls} = 488 \times 1.75 \]

### Step 4: Perform the multiplication for the number of girls.

Calculating:
\[ 488 \times 1.75 = 854 \]

So, the number of girls in the school is **854**.

### Final Answer:
The number of girls in the school is **854**.

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