3 Marks Question

Question 513 Marks

An electric pole casts a shadow of length $20$ metres at a time when a tree $6$ metres high casts a shadow of length $8$ metres. Find the height of the pole.
Hint. (height of the tree) : (length of the shadow)
= (height of the pole) : (length of its shadow).

Answer

Let the height of the pole be $x$ metres.
$\text{Now,}\frac{\text{height of the pole}}{\text{length of shadow of pole}}$
$=\frac{\text{height of thr tree}}{\text{Length of shadow of tree}}$
$\therefore\frac{\text{x}}{20}=\frac{6}{8}$
$\Rightarrow\text{x}=\frac{6}{8}\times20$
$=\frac{120}{8}=15$
$\therefore$ Height of the pole $= 15$ metres

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Question 523 Marks

Show that $48, 60, 75$ are in continued proportion.

Answer

Consider $48 : 60 : : 60 : 75$
Product of means $= 60 \times 60 = 3600$
Product of extremes $= 48 \times 75 = 3600$
So product of means = Product of extremes
Hence, $48, 60, 75$ are in continued proportion.

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Question 533 Marks

The ratio of income to expenditure of a family is $7 : 6$. Find the savings if the income is $Rs. 14000.$

Answer

Ratio in income and expenditure $= 7 : 6$
Total income $= Rs. 14000$
Let expenditure $= x,$
then $7 : 6 : : 14000 : \text{x}$
$\Rightarrow\text{x}=\frac{6\times14000}{7}=\text{Rs. }12000$
Savings = Total income - Expenditure $= \text{Rs. } 14000 - 12000$
$= \text{Rs. } 2000$

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Question 543 Marks

Write the following ratios in the simplest form: $3m \ 5\ cm : 35\ cm.$

Answer

To given ratio $= 3m 5\ cm : 35\ cm = (3 \times 100 + 5)cm : 35\ cm = 305\ cm : 35\ cm = 305 : 35 = 61 : 7$

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Question 553 Marks

Express the following ratios in the simplest form: $324 : 144$

Answer

The given ratio $=324:144=\frac{324}{144}$ To express it in simplest form, we divide the numerator and denominator by the $H.C.F$ of $324$ and $144.$
$H.C.F$ of $324$ and $144.$

$=36$
$\therefore\frac{324}{144}=\frac{324\div36}{144\div36}=\frac{9}{4}$
$\therefore \text{Required ratio}=9:4$

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Question 563 Marks

From the given pairs, find which ratio is larger: $(3 : 7)$ or $(4 : 9)$

Answer

$(3 : 7)$ or $(4 : 9)$
$\Rightarrow\frac{3}{7},\frac{4}{9}$
$\text{LCM of }7,9=63$
$\therefore\frac{3}{7}=\frac{3\times9}{7\times9}=\frac{27}{63}$
$\frac{4}{9}=\frac{4\times7}{9\times7}=\frac{28}{63}$
We see that $\frac{28}{63}>\frac{27}{63}\text{ or }\frac{4}{9}>\frac{3}{7}$
$\therefore4:9$ is greater ratio.

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Question 573 Marks

Mr Sahai and his wife are both school teachers and earn $Rs. 16800$ and $Rs. 10500$ per month respectively. Find the ratio of: Mrs Sahai’s income to her husband’s income.

Answer

Earning of Sahai $= Rs. 16800$
And of his wife $= Rs. 10500$
Then total income $= Rs. 16800 + 10500 = Rs. 27300$
Ratio in sahai's wife income and her husband's income. $= 10500 : Rs. 16800 = 5 : 8$
(Dividing by the $HCF$ of $10500$ and $16800 = 2100)$

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Question 583 Marks

Write the following ratios in the simplest form: $4\ kg : 2\ kg 500g$

Answer

The given ratio $= 4\ kg : 2\ kg 500g = (4 \times 1000)g : (2 \times 1000 + 500)g = 4000g : 2500g = 4000 : 2500 = 40 : 25 = 8 : 5$

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Question 593 Marks

Determine if the following ratios form a proportion: $2kg : 80kg$ and $25g : 625kg$

Answer

$2\ kg : 80\ kg$ and $25g : 625\ kg$
$\frac{2\text{kg}}{80\text{kg}}=\frac{1}{40}$ And
$\frac{25\text{g}}{625\text{kg}}=\frac{25}{625\times1000}$
$=\frac{1}{25000}$
$\because\frac{1}{40}\neq\frac{1}{25000}$
$\therefore 2\ kg : 80\ kg$ and $25g : 625\ kg$ are not in proportion.

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MATHS 3 Marks Question