Let's analyze the problem step-by-step.
Problem Restatement
- Rani distributes chocolates to her friends on her birthday.
- If she gives 8 chocolates to each friend , one friend will get only 7 chocolates.
- If she gives 7 chocolates to each friend , she will be left with 3 chocolates.
- We need to find how many friends she has.
Step 1: Define Variables
Let:
- nnn = number of friends
- TTT = total number of chocolates
Step 2: Translate Conditions into Equations
Condition 1: Giving 8 chocolates each, but one friend gets 7
If she tries to give 8 chocolates to each friend, but one friend gets only 7, that means:
- n−1n-1n−1 friends get 8 chocolates each
- 1 friend gets 7 chocolates
So total chocolates used:
T=8×(n−1)+7=8n−8+7=8n−1T=8\times (n-1)+7=8n-8+7=8n-1T=8×(n−1)+7=8n−8+7=8n−1
Condition 2: Giving 7 chocolates each, leftover 3 chocolates
If she gives 7 chocolates to each friend, leftover chocolates are 3:
T=7n+3T=7n+3T=7n+3
Step 3: Equate the two expressions for total chocolates TTT
8n−1=7n+38n-1=7n+38n−1=7n+3
8n−7n=3+18n-7n=3+18n−7n=3+1
n=4n=4n=4
Step 4: Find total chocolates TTT
Using n=4n=4n=4 in T=7n+3T=7n+3T=7n+3:
T=7×4+3=28+3=31T=7\times 4+3=28+3=31T=7×4+3=28+3=31
Final Answer:
Rani has 4 friends.
Verification
- If she gives 8 chocolates each: 3 friends get 8 chocolates = 24 chocolates, and 1 friend gets 7 chocolates, total 24+7=3124+7=3124+7=31.
- If she gives 7 chocolates each: 4×7=284\times 7=284×7=28, leftover 31−28=331-28=331−28=3.
Both conditions are satisfied. If you want, I can help with similar problems or explanations!
