# Excess and Shortage Questions

The objective of this math revision note is to enhance your child’s understanding and proficiency in solving excess and shortage questions.

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__Excess and Shortage Question 1__

__Excess and Shortage Question 1__

*Mrs Tan bought some sweets to distribute to her class. If she gives each student 6 sweets, she will have 8 sweets left. If she gives each student 8 sweets, she will be 6 sweets short. How many sweets does Mrs Tan have? *

**Solutions for (a)**

In the 1^{st} scenario, every student receives 6 sweets.

In the 2^{nd} scenario, every student receives 8 sweets.

Hence each student receives 2 more sweets in the 2^{nd} scenario than that of the 1^{st} scenario.

Difference in each student = 8 – 6 = 2

When we compare the total number of sweets in the 1^{st} scenario to that of the 2^{nd} scenario, we can see that the 2^{nd} scenario requires 14 more sweets.

Total difference = 8 + 6 = 14

Comparing the 2^{nd} scenario to that of the 1^{st} scenario:

Since every student gets 2 more sweets and they receive 14 more sweets in total, we can find the number of students as such:

14 ÷ 2 = 7 students

We can find the total number of sweets by either using the 1^{st} or 2^{nd} scenario:

Using 1^{st} scenario:

7 x 6 + 8 = 50 (Ans)

Using 2^{nd} scenario:

7 × 8 – 6 = 50 (Ans)

__Alternative solutions for (b)__

1u = the number of students

2u = 8 + 6 = 14

1u = 14 ÷ 2 = 7 students

We can find the total number of sweets by either using the 1^{st} or 2^{nd} scenario:

Using 1^{st} scenario:

7 × 6 + 8 = 50 (Ans)

Using 2^{nd} scenario:

7 × 8 – 6 = 50 (Ans)

__Excess and Shortage Question 2__

__Excess and Shortage Question 2__

*Tim packed 4 balls into each bag and found that he had 12 balls left over. If he packed 7 balls into each bag, he would need another 6 more balls. Find the number of bags he has. *

**Solutions**

Difference in each bag = 7 – 4 = 3

Each bag has 3 more balls in the 2^{nd} scenario compared to that of the 1^{st} scenario.

Total difference = 12 + 6 = 18

In the 2^{nd} scenario, the bags have 18 more balls in total compared to that of the 1^{st} scenario.

Comparing the 2^{nd} scenario to that of the 1^{st} scenario:

Since every bag has 3 more balls and the bags receive 18 more balls in total, we can find the number of bags as such:

Number of bags = 18 ÷ 3 = 6 bags (Ans)

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