How many multiples of $4$ lie between $10$ and $250 ?$

60

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70

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80

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90

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Solution

The correct option is B
Clearly, the numbers between $10$ and $250$ which are multiple of $4$ are $12, 16, 20, . . ., 248$ .
This is an AP with first term $a = 12$ , common difference $d = 4$ .
Let there be $n$ terms in this AP, then
$a_{n} = 248$
$\Rightarrow a + (n - 1) d = 248$
$\Rightarrow 12 + (n - 1) \times 4 = 248$
$\Rightarrow (n - 1) \times 4 = 248 - 12$
$\Rightarrow (n - 1) \times 4 = 236$
$\Rightarrow (n - 1) = 59$
$\Rightarrow n = 60$
Hence, 60 multiples of 4 lie between 10 and 250.

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How many multiples of 4 lie between 10 and 250 ?

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How many multiples of 4 lie between 10 and 250?

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