Answer
Verified
478.5k+ views
Hint: We can use the divisibility rule for the numbers 3 and 5 to solve this question. In the case of number 5, the value of b can only be either 0 or 5. Similarly, we can apply conditions for number 3 also and get to a conclusion.
Complete step-by-step answer:
Before proceeding we should know the divisibility rule of 3 as well as 5. These are as follows:
Divisibility rule of 3: A number is divisible by 3 if and only if the sum of the digits of a number is divisible by 3.
Divisibility rule of 5: A number is divisible by 5 if and only if the last digit of a number is either 0 or 5.
Therefore, the number 2345 a 60b is divisible by 5 only if the value of $b=0\text{ or 5}$.
We have to take the value of b as 5 as we have been asked the maximum value of $a+b$.
Then the sum of the digits of the given number 2345 a 60b is $25+a$.
Therefore, the numbers greater than 25 and divisible by 3 are 20, 30, 35.
Hence, the value of a maybe 2, 5, 8 .
By comparing, the possible values of a, we get that the maximum value of $a=8$
Therefore, we have $a=8,b=5$.
Hence, the maximum value of $a+b$ is $13$.
Hence, the answer is option (b).
Note: Always remember we have been asked for the maximum value of $a+b$, therefore for the number to be divisible by 5, the last digit must be 5 not 0 as we have been asked the maximum value of $a+b$. Make sure that after getting the maximum values of $a+b$, check at least once the number is divisible by both 3 and 5.
Complete step-by-step answer:
Before proceeding we should know the divisibility rule of 3 as well as 5. These are as follows:
Divisibility rule of 3: A number is divisible by 3 if and only if the sum of the digits of a number is divisible by 3.
Divisibility rule of 5: A number is divisible by 5 if and only if the last digit of a number is either 0 or 5.
Therefore, the number 2345 a 60b is divisible by 5 only if the value of $b=0\text{ or 5}$.
We have to take the value of b as 5 as we have been asked the maximum value of $a+b$.
Then the sum of the digits of the given number 2345 a 60b is $25+a$.
Therefore, the numbers greater than 25 and divisible by 3 are 20, 30, 35.
Hence, the value of a maybe 2, 5, 8 .
By comparing, the possible values of a, we get that the maximum value of $a=8$
Therefore, we have $a=8,b=5$.
Hence, the maximum value of $a+b$ is $13$.
Hence, the answer is option (b).
Note: Always remember we have been asked for the maximum value of $a+b$, therefore for the number to be divisible by 5, the last digit must be 5 not 0 as we have been asked the maximum value of $a+b$. Make sure that after getting the maximum values of $a+b$, check at least once the number is divisible by both 3 and 5.
Recently Updated Pages
Change the following sentences into negative and interrogative class 10 english CBSE
A Paragraph on Pollution in about 100-150 Words
One cusec is equal to how many liters class 8 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What were the social economic and political conditions class 10 social science CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE
Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
How do you graph the function fx 4x class 9 maths CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE
What is the past participle of wear Is it worn or class 10 english CBSE
Why did the British treat the Muslims harshly immediately class 10 social science CBSE
A Paragraph on Pollution in about 100-150 Words