2 Marks Questions

Question 12 Marks

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

Answer

Ratio $= 2 : 7$ The 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 $= 33 \times 88 = 2904$
Product of means $= 44 \times 66 = 2904$
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 $= 7: 8$ Consequent
$8x = 40$
$\text{x}=\frac{40}{8}$
$x = 5$
Antecedent $= 7x = 7 \times 5 = 35$

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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 $= 46 \times 46 = 2116$
Product of means $= 69 \times 69 = 4761$
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 $= 72 \times 217 = 15624$
Product of means $= 84 \times 186 = 15624$
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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