3 Mark Question

Question 13 Marks

Vijaya wanted to gift pens to seven of her friends on her birthday. When she went to a shop to buy them, the shopkeeper told her the rate for a dozen pens.
i. Can you help Vijaya to find the cost of 7 pens?
ii. If you find the cost of one pen, you can also find the cost of 7, right?

Answer

Cost of 12 pens = Rs 84.
∴ Cost of 12 pens
$=\frac{\text { Cost of } 12 \text { pens }}{12}=\frac{84}{12}=₹ 7$
∴ Cost of 7 pens = Cost of one pen x Number of pens = 7 × 7
∴ Cost of 7 pens = Rs 49
∴ The cost of 7 pens (Rs 49) can be found by unitary method.

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Question 23 Marks

Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is younger than his father by 6 years. Find the following ratios.
i. Ratio of Shubham’s age today to his mother’s age today.
ii. Ratio of Shubham’s mother’s age today to his father’s age today.
iii. The ratio of Shubham’s age to his mother’s age when Shubham was 10 years old.

Answer

Shubham’s age today = 12 years
Shubham’s father’s age = 42 years
Shubham’s mother age = Shubham’s father’s age – 6 years
= 42 years – 6 years = 36 years

i. Ratio of Shubham’s age today to his mother’s age today
$\begin{aligned} & =\frac{\text { Shubham's age today }}{\text { Shubham's Mother's age today }} \\ & =\frac{12}{36}=\frac{12 \div 12}{36 \div 12}=\frac{1}{3}\end{aligned}$
∴ The ratio of Shubham’s age today to his mother’s age today is $\frac{1}{3}$.

ii. Ratio of Shubham’s mother age today to his father’s age today
$\begin{aligned} & =\frac{\text { Shubham's mother's age today }}{\text { Shubham's father's age today }} \\ & =\frac{36}{42}=\frac{36 \div 6}{42 \div 6}=\frac{6}{7}\end{aligned}$
∴ The ratio of Shubham’s mother’s age today to his father’s age today is $\frac{6}{7}$.

iii. Shubham’s age today is 12 years and his mothers age is 36 years.
Hence when Shubham’s age was 10 years, his mother’s age was 34 years (i.e. 36 – 2 years).
Ratio of Shubham’s age to his mother’s age when Shubham was 10 years old
$=\frac{\text { Shubham'sage }}{\text { Shubham's mother'sage }}=\frac{10}{34}=\frac{10 \div 2}{34 \div 2}=\frac{5}{17}$
∴ The ratio of Shubham’s age to his mother’s age when Shubham was 10 years old is $\frac{5}{17}$.

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Question 33 Marks

Snehal has a red ribbon that is 80 cm long and a blue ribbon 2.20 m long. What is the ratio of the length of the red ribbon to that of the blue ribbon?

Answer

1 metre =100 cm
Length of the red ribbon = 80 cm
Length of the blue ribbon = 2.20 m = 2.20 x 100 cm
$\begin{aligned} & =\frac{220}{100} \times \frac{100}{1}=\frac{220 \times 100}{100 \times 1} \\ & =220 cm \end{aligned}$

∴ Ratio of length of the red ribbon to that of the blue ribbon
$\begin{aligned} & =\frac{\text { Length of red ribbon }}{\text { Length of blue ribbon }} \\ & =\frac{80 cm }{220 cm }=\frac{80 \div 20}{220 \div 20}=\frac{4}{11}\end{aligned}$

∴ The ratio of the length of the red ribbon to that of the blue ribbon is $\frac{4}{11}$.

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Question 43 Marks

In the figure, colour some squares with any colour you like and leave some blank.

i. Find the ratio of the colored boxes to the blank ones.
ii. Find the ratio of the colored boxes to the total boxes.
iii. Find the ratio of the blank boxes to the total boxes.

Answer

i. Ratio of the colored boxes to the blank ones
$=\frac{\text { Number of coloured boxes }}{\text { Number of blank boxes }}=\frac{7}{9}$
ii. Ratio of the colored boxes to the total boxes
$=\frac{\text { Number of coloured boxes }}{\text { Number of total boxes }}=\frac{7}{16}$
iii. Ratio of the blank boxes to the total boxes
$=\frac{\text { Number of blank boxes }}{\text { Number of total boxes }}=\frac{9}{ 1 6 }$

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Question 53 Marks

In the figure, colour some squares with any colour you like and leave some blank.

i. Count all the boxes and write the number.
ii. Count the colored ones and write the number.
iii. Count the blank ones and write the number.

Answer

i. The number of all boxes is 16.
ii. The number of colored boxes is 7.
iii. The number of blank boxes is 9.

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