4 Mark Question

Question 14 Marks

If n varies directly as m, complete the following table.

m	3	5	6.5	__	1.25
n	12	20	__	28	__

Answer

Given, n varies directly as m
∴ n ∝ m
∴ n = km …(i)
where, k is the constant of variation

i. When m = 3, n = 12
∴ Substituting m = 3 and n = 12 in (i), we get
n = km
∴ 12 = k × 3
$\therefore k=\frac{12}{3}$
∴ k = 4
Substituting, k = 4 in (i), we get
n = km
∴ n = 4m …(ii)
This is the equation of variation.

ii. When m = 6.5, n = ?
∴ Substituting, m = 6.5 in (ii), we get
n = 4m
∴ n = 4 × 6.5
∴ n = 26

iii. When n = 28, m = ?
∴ Substituting, n = 28 in (ii), we get
n = 4m
∴ 28 = 4m
∴ 28 = 4m
$\therefore m=\frac{28}{4}$
∴ m = 7

iv. When m = 1.25, n = ?
∴ Substituting m = 1.25 in (ii), we get
n = 4m
∴ n = 4 × 1.25
∴ n = 5

m	3	5	6.5	7	1.25
n	12	20	26	28	5

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Question 24 Marks

If m ∝ n and when m = 154, n = 7. Find the value of m, when n = 14.

Answer

Given that,
$
\begin{aligned}
& \mathrm{m} \propto \mathrm{n} \\
& \therefore \mathrm{m}=\mathrm{kn} . . \text { (i) }
\end{aligned}
$
where $\mathrm{k}$ is constant of variation.
When $m=154, n=7$
$\therefore$ Substituting $m=154$ and $n=7$ in (i), we get
$
\begin{aligned}
& \mathrm{m}=\mathrm{kn} \\
& \therefore 154=\mathrm{k} \times 7 \\
& \therefore k=\frac{154}{7} \\
& \therefore \mathrm{k}=22
\end{aligned}
$
Substituting $k=22$ in (i), we get
$
\begin{aligned}
& \mathrm{m}=\mathrm{kn} \\
& \therefore \mathrm{m}=22 \mathrm{n} \text {...(ii) }
\end{aligned}
$
This is the equation of variation.
When $n=14, m=?$
$\therefore$ Substituting $n=14$ in (ii), we get
$
\begin{aligned}
& \mathrm{m}=22 \mathrm{n} \\
& \therefore \mathrm{m}=22 \times 14 \\
& \therefore \mathrm{m}=308
\end{aligned}
$

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