2 Mark Question

Question 12 Marks

Divide Rs. 351 into two parts such that one may be to the other as 2 : 7.

Answer

Ratio = 2 : 7The sum of the terms in the ratio = 2 + 7 = 9
First ratio $=\frac29\times351$
$=2\times39$
$=\text{Rs. }78$
Second ratio $=\frac{7}{9}\times351$
$=7\times39$
$=\text{Rs. }273$

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Question 22 Marks

Find which of the following are in proportion?
33, 44, 66, 88

Answer

We have,
Product of extremes = 33 × 88 = 2904
Product of means = 44 × 66 = 2904
Therefore, the product of the extremes is equal to the product of the means.
Hence, 33, 44, 66, 88 are in proportion.

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Question 32 Marks

A sum of Rs. 5500 is to be divided between Raman and Amen in the rate 2 : 3. How much will each get?

Answer

We have,Sum of the terms in the ratio = 2 + 3 = 5
Raman share $=\frac25\times5500$
$=2\times1100$
$=\text{Rs. }2200$
Aman share $=\frac35\times5500$
$=3\times1100$
$=\text{Rs. }3300$

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Question 42 Marks

In the ratio 7 : 8. If the consequent is 40, what a the antecedent?

Answer

Given ratio = 7: 8Consequent
8x = 40
$\text{x}=\frac{40}{8}$
x = 5
Antecedent = 7x = 7 × 5 = 35

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Question 52 Marks

Find x in the following proportions:
16 : 18 = x : 96

Answer

16 : 18 = x : 96$\frac{16}{18}=\frac{\text{x}}{96}$
$\text{x}=\frac{256}{3}$

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Question 62 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

Answer

Height of the tree : Length of the shadow of tree Height of the pole : Length of the shadow of pole$\text{x}: 20 = 6: 8$
$\text{x} = \frac{120}8$
$\text{x} = 15\text{m}$

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Question 72 Marks

Find x in the following proportions:
x : 92 = 87 : 116

Answer

x : 92 = 87 : 116$\frac{\text{x}}{92}=\frac{87}{116}$
$\text{x}=\frac{\text{87}\times92}{116}$
$\text{x}=69$

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Question 82 Marks

Find which of the following are in proportion?
46, 69, 69, 46

Answer

We have,
Product of extremes = 46 × 46 = 2116
Product of means = 69 × 69 = 4761
Therefore, the product of the extremes is equal to the product of the means.
Hence, 46, 69, 69, 46 are not in proportion.

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Question 92 Marks

Find which of the following are in proportion?
72, 84, 186, 217

Answer

We have,
Product of extremes = 72 × 217 = 15624
Product of means = 84 × 186 = 15624
Therefore, the product of the extremes is equal to the product of the means.
Hence, 72, 84, 186, 217 are in proportion.

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