Delhi Police Constable Exam Model Paper 3

GIVEN:
Numbers between 31 and 491
FORMULA USED:
${\mathit{N}}^{\mathit{t}\mathit{h}}\mathit{t}\mathit{e}\mathit{r}\mathit{m}={\mathit{T}}_{\mathit{n}}=\mathit{a}+\left(\mathit{n}\mathit{–}1\right)\mathit{d}$
CALCULATION:
Numbers which are divisible by both 3 and 5 = Numbers which are divisible by 15.
Numbers between 31 and 491 which are divisible by 15 = 45, 60, 75, 90, …………., 480
Let ‘n’ numbers are divisible by 15.
Now, $480=45+\left(\mathit{n}\mathit{–}1\right)\times 15$
⇒ $15\left(\mathit{n}\mathit{–}1\right)=435$
⇒ $\left(\mathit{n}\mathit{–}1\right)=29$
⇒ $\mathit{n}=30$
Hence, total numbers = 30