Question
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
✓
Answer
A number N is dividend by 7 leaves a remainder 4.
$\therefore\text{N}=7\text{q}+4$
N can take values 4, 11, 18, ..... 998
Now,
4, 11, 18, ..... 998 are arithmetic progression.
First term $\text{A}=4$
Common differnce $\text{d}=7$
Last term $\text{l}=998$
We know thet,
$\text{l}=\text{a}(\text{n}-1)\text{d}$
$\Rightarrow998=4+(\text{n}-1)7$
$\Rightarrow998=4+7\text{n}-1$
$\Rightarrow998=7\text{n}-3$
$\Rightarrow1001=7\text{n}$
$\Rightarrow\text{n}=\frac{1001}{7}$
$\Rightarrow\text{n}=143$
Hence, 143 numbers are there between 1 and 1000 which when divided by 7 leave remainder4.
$\therefore\text{N}=7\text{q}+4$
N can take values 4, 11, 18, ..... 998
Now,
4, 11, 18, ..... 998 are arithmetic progression.
First term $\text{A}=4$
Common differnce $\text{d}=7$
Last term $\text{l}=998$
We know thet,
$\text{l}=\text{a}(\text{n}-1)\text{d}$
$\Rightarrow998=4+(\text{n}-1)7$
$\Rightarrow998=4+7\text{n}-1$
$\Rightarrow998=7\text{n}-3$
$\Rightarrow1001=7\text{n}$
$\Rightarrow\text{n}=\frac{1001}{7}$
$\Rightarrow\text{n}=143$
Hence, 143 numbers are there between 1 and 1000 which when divided by 7 leave remainder4.
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