Exercise 4.1 - Chapter 4 Direct and Inverse Proportion Term 1 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $4.1$
Fill in the blanks.
(i) If the cost of 8 apples is 56 then the cost of 12 apples is
(ii) If the weight of one fruit box is $3 \frac{1}{2} \mathrm{~kg}$, then the weight of 6 such boxes is
(iii) A car travels $60 \mathrm{~km}$ with 3 liters of petrol. If the car has to cover the distance of $200 \mathrm{~km}$, it requires ___ liters of the petrol.
(iv) If $7 \mathrm{~m}$ cloth costs $₹ 294$, then the cost of $5 \mathrm{~m}$ of cloth is
(v) If a machine in a cool drinks factory fills 600 bottles in $5 \mathrm{hrs}$, then it will fill bottles in 3 hours.
Solutions:
(i) 84
(ii) $21 \mathrm{~kg}$
(iii) 10
(iv) ₹ 210
(v) 360

Question 2 .
Say True or False
(i) Distance travelled by a bus and time taken are in direct proportion.
(ii) Expenditure of a family to number of members of the family are in direct proportion.
(iii) Number of students in a hostel and consumption of food are not in direct proportion.
(iv) If Mallika walks $1 \mathrm{~km}$ in 20 minutes, then she can convert $3 \mathrm{~km}$ in 1 hour.
(v) If 12 men can dig a pond in 8 days, then 18 men can dig it in 6 days.
Solutions:
(i) True
(ii) True
(iii) False
(iv) True

(v) False

Question $3 .$
A dozen bananas costs ₹ 20 . What is the price of 48 bananas ?
Solution:
Let the required price be $₹ x$. As the number of bananas increases price also increases $\therefore$ Number of bananas and cost are in direct proportion.

\begin{aligned}
\frac{x_{1}}{y_{1}} &=\frac{x_{2}}{y_{2}} \\
\frac{12}{20} &=\frac{48}{x} \\
x &=\frac{48 \times 20}{12} \\
x &=80 \\
\therefore \quad \text { Price of } 48 \text { bananas } &=₹ 80 .
\end{aligned}

Question $4 .$
A group of 21 students paid $₹ 840$ as the entry fee for a magic show. How many students entered the magic show if the total amount paid was $₹ 1680$ ?
Solution:
Let the required number of students be $x$.

As the number of students increases the entry fees also increases.
$\therefore$ They are in direct proportion.

$\begin{aligned}
\therefore \quad \frac{x_{1}}{y_{1}} &=\frac{x_{2}}{y_{2}} \\
\frac{21}{840} &=\frac{x}{1680} \\
x &=\frac{21 \times 1680}{840} \\
x &=42 .
\end{aligned}$
$\therefore$ The number of students entered magic show $=42$

Question $5 .$
A birthday party is arranged in third floor of a hotel. 120 people take 8 trips in a lift to go to the party hall. If 12 trips were made how many people would have attended the party?
Solution:
Let the number of people attended the party be $x$.

As the number of trips increases, number of people also increases.
$\therefore$ They are in direct proportion.
$\begin{aligned}
\frac{x_{1}}{y_{1}} &=\frac{x_{2}}{y_{2}} \\
\frac{120}{8} &=\frac{x}{12} \\
x &=\frac{120 \times 12}{8}=180
\end{aligned}$
180 people attend the party in 12 trips

Question 6

The shadow of a pole with height of 8m is 6m. If the shadow of another pole measured at the same time is 30m, find the height of the pole? Solution: Let the required height of the pole be ‘x’ m

\begin{aligned}
&\text { Height of the pole and its shadow are in direct proportion }\\
&\therefore \quad \frac{x_{1}}{y_{1}}=\frac{x_{2}}{y_{2}}
\end{aligned}

\begin{aligned}
\frac{8}{6} &=\frac{x}{30} \\
x &=\frac{8 \times 30}{6} \\
x &=40
\end{aligned}

Question $7 .$
A postman can sort out 738 letters in 6 hours. How many letters can be sorted in 9 hours?
Solution:
Let the required number of letters be $\mathrm{x}$.

They are in direct proportion.
$\begin{aligned}
\frac{x_{1}}{y_{1}} &=\frac{x_{2}}{y_{2}} \\
\frac{738}{6} &=\frac{x}{9} \\
x &=\frac{739}{6} \times 9 \\
x &=1107
\end{aligned}$
In 9 hours 1107 letters can be sorted.

Question 8 .
If half a meter of cloth costs $₹ 15$. Find the cost of $8 \frac{1}{3}$ meters of the same cloth.
Solution:

Let the cost of cloth required be $x$.

Cost and length are in direct proportion.
$\begin{aligned}
\therefore \frac{x_{1}}{y_{1}} &=\frac{x_{2}}{y_{2}} ; \quad \frac{15}{\frac{1}{2}}=\frac{x}{\frac{25}{3}} \\
15 \times \frac{25}{3} &=x \times \frac{1}{2} \\
x \times \frac{1}{2} &=125 \\
x &=125 \times 2 \\
x &=250 \\
\therefore \quad \text { Cost of } 8 \frac{1}{3} \mathrm{~m} \text { of cloth } &=₹ 250 .
\end{aligned}$

Question $9 .$
The weight of 72 books is $9 \mathrm{~kg}$. What is the weight of 40 such books (using unitary method)
Solution:
Weight of 72 books $=9 \mathrm{~kg}=9000 \mathrm{~g}$
$\therefore$ Weight of 1 book $=\frac{9000}{72}=125 \mathrm{~g}$
$\therefore$ Weight of 40 books $=125 \times 40 \mathrm{~g}=5000 \mathrm{~g}=5 \mathrm{~kg}$.
Weight of 40 books $=5 \mathrm{~kg}$
 

Question 10 .
Thamarai pages $₹ 7500$ as rent for 3 months. With the same rate how much does she have to pay for 1 year (using unitary method).
Solution:
Rent paid by Thamarai for 3 months $=₹ 7500$
$\therefore$ Rent paid for 1 month $=\frac{7500}{3}=2500$
Rent paid for 1 year or 12 moths $=2500 \times 12=₹ 30,000$
For 1 year rent to be paid $=₹ 30,000$

Question $11 .$
If 30 men can reap a field in 15 days, then in how many days can 20 men reap the same field? (using unitary method).
Solution:
30 men can reap a field in 15 days.
$\therefore 1$ men can reap the field in $\frac{15}{30}$ days $=\frac{1}{2}$ days.
$\therefore 20$ men can reap the field in $=\frac{1}{2} \times 20=10$ days
$\therefore 20$ men can reap the field in 10 days.

Question $12 .$
Valli purchase 10 pens for $₹ 180$ and Kamala boys 8 pens for $₹ 96$. Can you say who bought the pen cheaper (using unitary method).
Solution:
Valli purchases 10 pens for $₹ 180$
$\therefore$ Valli purchase 1 pen for $₹ \frac{180}{10}=₹ 18$
Kamala buys 8 pens for $₹ 96$
$\therefore$ Kamala buys 1 pen for $₹ \frac{96}{8}=₹ 12$
$₹ 12<₹ 18$
$\therefore$ Kamala bought the pen cheaper.

Question $13 .$
A motorbike requires 2 liters of petrol to cover 100 kilometres. How many liters of petrol will be required to cover 250 kilometers? (using unitary method).
Solution:
To cover $100 \mathrm{~km}$ quantity of petrol required $=2$ litres
$\therefore \quad$ To cover $1 \mathrm{~km}$ petrol required $=\frac{2}{100}=\frac{1}{50}$ litres
$\therefore \quad$ To cover $250 \mathrm{~km}$ petrol required $=\frac{1}{50} \times 250=5$ litres.
5 litres of petrol required to cover $250 \mathrm{~km}$

Objective Type Questions

Question $14 .$
If the cost of 3 books is $₹ 90$, then find the cost of 12 books.
(i) ₹ 300
(ii) ₹ 320
(iii) ₹ 360
(iv) $₹ 400$
Hint $: \frac{3}{90}=\frac{12}{x} \Rightarrow x=\frac{12 \times 90}{\not 3}=360$
Solution:
(iii) $₹ 360$

Question $15 .$
If Mani buys $5 \mathrm{~kg}$ of potatoes for $₹ 75$ then he can buy $₹ 105$.
(i) 6
(ii) 7
(iii) 8
(iv) 5
Solution:
(ii) 7

Question $16 .$
35 cycles were produced in 5 days by a company then cycles will be produced in 21 days.
(i) 150
(ii) 70
(iii) 100
(iv) 147
Hint $: \frac{35}{5}=\frac{x}{21} \Rightarrow x=\frac{\not 25 \times 21}{\not 5}=147$
Solution:
(iv) 147

Question $17 .$
An aircraft can accommodate 280 people in 2 trips. It can take trips to take 1400 people.

(i) 8
(ii) 10
(iii) 9
(iv) 12
Solution:
(ii) 10

Question $18 .$
Suppose $3 \mathrm{~kg}$ of sugar is used to prepare sweets for 50 members, then___ $\mathrm{kg}$ of sugar is required for 150 members.
(i) 9
(ii) 10
(iii) 15
(iv) 6

Solution:

(i) 9