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Q.

Of all the choices given below, find the sum of all multiples of 9 lying between 300 and 700.


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a

21,978

b

20,789

c

22,232

d

29,546 

answer is A.

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Detailed Solution

We have to find the sum of all multiples of 9 lying between 300 and 700.
The multiples of 9 lying between 300 and 700 are:
306, 315, 324,…, 693
The above numbers are in the form of an AP.
So,
a=306, d=9, a n =693
We know that,
a n =a+ n−1 d
Substitute the known values in the formula,
306+(n−1)×9=693 306+9n−9=693 297+9n=693 9n=396 n=44
There are 44 three-digit numbers that are multiples of 9 between 300 and 700.
We know that,
S n = n 2 [a+l]
where l is the last term = a n =693 .
Substitute the known values in the above formula,
S 29 = 44 2 [306+693]
=22(999) =21,978
The sum of the numbers that are multiples of 9 between 300 and 700 is 21,978.
Hence option 1) is correct.
 
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Of all the choices given below, find the sum of all multiples of 9 lying between 300 and 700.