If the seven-digit number 876p37q is divisible by
225, then the values of p and q respectively are

Question

Accepted Answer

To find the values of $$ p $$ and $$ q $$ such that the seven-digit number $$ 876p37q $$ is divisible by 225, we ensure the number satisfies divisibility by both 9 and 25 (since $$ 225 = 9 	imes 25 $$).

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### Step 1: Divisibility by 25  
A number is divisible by 25 if its last two digits form a number divisible by 25.  
For $$ 876p37q $$, the last two digits are $$ 7q $$. To satisfy divisibility by 25:  
$$
7q = 75 \quad (	ext{as } q = 5)
$$  
Thus, $$ q = 5 $$.

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### Step 2: Divisibility by 9  
A number is divisible by 9 if the sum of its digits is divisible by 9. For $$ 876p375 $$, the sum of its digits is:  
$$
8 + 7 + 6 + p + 3 + 7 + 5 = 36 + p
$$  
To satisfy divisibility by 9:  
$$
36 + p \equiv 0 \pmod{9}
$$  
Since $$ 36 \div 9 = 4 $$, $$ p = 0 $$.

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### Final Answer:  
The values of $$ p $$ and $$ q $$ are **0** and **5**, respectively.

Answer

Answer

Answer