A total of 120 students gave the entrance test.

out of all failures 9 were males

out of all passed students 53 were females

Laddu was very happy after he cleared this entrance test.

Let's break down the information provided:

- A total of 120 students took the entrance test.
- Out of all the students who failed, 9 were males.
- Out of all the students who passed, 53 were females.
- Laddu was among the students who passed the test.

### Let's define some terms to solve this problem:

Let:
- \( P_m \) = number of males who passed.
- \( P_f = 53 \) = number of females who passed.
- \( F_m = 9 \) = number of males who failed.
- \( F_f \) = number of females who failed.
- \( N_m \) = total number of males.
- \( N_f \) = total number of females.
- \( T = 120 \) = total number of students.

### Step-by-step solution:

1. **Total number of students who passed the test:**
   Since 53 females passed, and we don't know how many males passed, we denote the total number of students who passed as:
   \[
   P = P_m + 53
   \]
   Let \( F \) represent the number of students who failed. Then:
   \[
   F = F_m + F_f = 9 + F_f
   \]

2. **Total number of students:**
   The sum of students who passed and students who failed must equal the total number of students who took the test:
   \[
   P + F = 120
   \]
   Substituting \( P \) and \( F \) into this equation:
   \[
   (P_m + 53) + (9 + F_f) = 120
   \]
   Simplifying:
   \[
   P_m + 53 + 9 + F_f = 120
   \]
   \[
   P_m + F_f = 58
   \]

3. **Total number of males and females:**
   The total number of males is the sum of males who passed and males who failed:
   \[
   N_m = P_m + 9
   \]
   The total number of females is the sum of females who passed and females who failed:
   \[
   N_f = 53 + F_f
   \]
   The total number of students is:
   \[
   N_m + N_f = 120
   \]
   Substituting the expressions for \( N_m \) and \( N_f \):
   \[
   (P_m + 9) + (53 + F_f) = 120
   \]
   Simplifying:
   \[
   P_m + F_f = 58
   \]
   This matches the previous equation, so we have \( P_m + F_f = 58 \).

This means there are **58 males who passed or females who failed**, but to break it down further would require additional data about either the exact number of males who passed or females who failed.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How many students in total passed the entrance test?
2. What is the ratio of males to females among the students?
3. If Laddu is a male, how can we calculate the total number of males?
4. How does the number of passed females compare to failed males?
5. If all passed students received a prize, how many prizes were distributed?

**Tip:** Always verify the total by adding the individual components to ensure consistency with the overall number of participants.

A total of 120 students gave the entrance test. Out of all failures, 9 were males. Out of all passed students, 53 were females. Laddu was very happy after he cleared this entrance test.

Analyze the entrance test results where 120 students participated. Explore how many males and females passed or failed the test, using basic algebraic concepts to break down the number of students and solve for unknowns. Perfect for students in Grades 5-7.

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