3 Mark 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 × 60 = 3600
Product of extremes = 48 × 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 5cm : 35cm.

Answer

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

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Question 553 Marks

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

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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:
4kg : 2kg 500g

Answer

The given ratio = 4kg : 2kg 500g
= (4 × 1000)g : (2 × 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

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

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Maths 3 Mark Question