Exercise 1.5 - Chapter 1 Number Systems Term 1 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question $1 .$
One night in Kashmir, the temperature is $-5^{\circ} \mathrm{C}$. Next day the temperature is $9^{\circ} \mathrm{C}$. What is the increase in temperature?
Solution:
Temperature in the first day $=-5^{\circ} \mathrm{C}$
Temperature in the next day $=9^{\circ} \mathrm{C}$
$\therefore$ Increase in temperature $=9^{\circ} \mathrm{C}-\left(-5^{\circ} \mathrm{C}\right)$
$=9^{\circ} \mathrm{C}+\left(+5^{\circ} \mathrm{C}\right)=14^{\circ} \mathrm{C}$

Question $2 .$
An atom can contain protons which have a positive charge $(+)$ and electrons which have a negative charge $(-)$. When an electron and a proton pair up, they become neutral $(0)$ and cancel the charge at. Now determine the net charge:
(i) 5 electrons and 3 protons $\rightarrow-5+3=-2$ that is 2 electrons $\ominus \ominus$
(ii) 6 protons and 6 electrons $\rightarrow$
(iii) 9 protons and 12 electrons $\rightarrow$
(iv) 4 protons and 8 electrons $\rightarrow$
(v) 7 protons and 6 electrons $\rightarrow$
Solution:
(ii) 6 protons and 6 electrons $\rightarrow(+6)+(-6)=0$
(iii) 9 protons and 12 electrons $\rightarrow(+9)+(-12)=9-12=-3 \Rightarrow 3$ electrons $\ominus \ominus \ominus$
(iv) 4 protons and 8 electrons $\rightarrow(+4)+(-8)=+4-8=-4 \Rightarrow 4$ electrons $\ominus \ominus \ominus \ominus$
(v) 7 protons and 6 electrons $\rightarrow(+7)+(-6)=+1=1$ proton $\oplus$

Question $3 .$
Scientists use the Kelvin scale $(\mathrm{K})$ as an alternative temperature scale to degrees Celsius $\left({ }^{\circ} \mathrm{C}\right)$ by the relation $\mathrm{T}^{\circ} \mathrm{C}=(\mathrm{T}+273) \mathrm{K}$. Convert the following to Kelvin:
(i) $-275^{\circ} \mathrm{C}$
(ii) $45^{\circ} \mathrm{C}$

(iii) $-400^{\circ} \mathrm{C}$
(iv) $-273^{\circ} \mathrm{C}$
Solution:
(i) $-275^{\circ} \mathrm{C}=(-275+273) \mathrm{K}=-2 \mathrm{~K}$
(ii) $45^{\circ} \mathrm{C}=(45+273) \mathrm{K}=318 \mathrm{~K}$
(iii) $-400^{\circ} \mathrm{C}=(-400+273) \mathrm{K}=-127 \mathrm{~K}$
(iv) $-273^{\circ} \mathrm{C}=(-273+273) \mathrm{K}=0 \mathrm{~K}$

Question $4 .$
Find the amount that is left in the student's bank account, if he has made the following transaction in a month. His initial balance is ₹ 690 .
(i) Deposit ( $+$ ) of ₹ 485
(ii) Withdrawal (-) of $₹ 500$
(iii) Withdrawal (-) of ₹ 350
(iv) Deposit (+) of ₹ 89
(v) If another ₹ 300 was withdrawn, what would the balance be?
Solution:
(i) Initial balance of student's account $=₹ 690$
Deposited amount $=₹ 485(+)$
$\therefore$ Amount left in the account $=₹ 690+₹ 485=₹ 1175$
(ii) Balance in the account $=₹ 1175$
Amount withdrawn $=₹ 500(-)$
Amount left $=₹ 1175-₹ 500=₹ 675$
(iii) Balance in the account $=₹ 675$
Amount withdrawn $=₹ 350(-)$
Amount left $=₹ 675-₹ 350=₹ 325$
(iv) Balance in the account $=₹ 325$
Amount deposited $=₹ 89(+)$
Amount left $=₹ 325+₹ 89=₹ 414$
(v) Balance in the account $=₹ 414$
Amount withdrawn $=₹ 300(-)$
Amount left $=₹ 414-₹ 300=₹ 114$

Question $5 .$
A poet Tamizh Nambi lost 35 pages of his 'lyrics' when his file had got wet in the rain. Use integers, to determine the following.
(i) If Tamil Nambi wrote 5 pages per day, how many day's work did he lose?

(ii) If four pages contained 1800 characters, (letters) how many characters were lost?
(iii) If Tamil Nambi is paid ₹ 250 for each page produced, how much money did he lose?
(iv) If Kavimaan helps Tamizh Nambi and they are able to produce 7 pages per day, how many days will it take to recreate the work lost?
(v) Tamizh Nambi pays Kavimann ₹ 100 per page for his help. How much money does Kavimaan receive?
Solution:
Total pages lost $-35$
One day work $=5$ page 35
35 pages $=\frac{35}{5}=7$ days work
$\therefore 7$ day's work he lost.
(ii) Number of characters in four pages $=1800$
Number of characters in one page $=\frac{1800}{4}=450$
$\therefore$ Number of characters in 35 pages $=450 \times 35=15,750$ characters
(iii) Payment for one page $=₹ 250$
$\therefore$ Payment for 35 pages $=₹ 250 \times ₹ 35=₹ 8,750$
(iv) Number of pages recreated a day $=7$
$\therefore$ To recreate 35 pages day's needed $=\frac{35}{7}=5$ days
(v) Payment of Kavimaan $=₹ 100$ per page
$\therefore$ for 35 pages payment $=₹ 100 \times 35=₹ 3,500$

Question $6 .$
Add 2 to me. Then multiply by 5 and subtract 10 and divide new by 4 and I will give you $15 !$ Who am I?
Solution:
According to the problem $\{[(\mathrm{I}+2) \times 5]-10\} \div 4=15$
$\begin{aligned}
&\{[(\mathrm{I}+2) \times 5]-10\}=15 \times 4=60 \\
&\mathrm{I}+2=\frac{70}{5}=14 \\
&(\mathrm{I}+2) \times 5=60+10=70 \\
&\mathrm{I}=14-2 ; \mathrm{I}=12
\end{aligned}$
 

Question $7 .$
Kamatchi, a fruit vendor sells 30 apples and 50 pomegranates. If she makes a profit of ? 8 per apple and loss ? 5 per pomegranate. What will be her overall profit or loss?
Solution:
Number of apples Kamatchi sold $=30$
Profit per apple $=₹ 8(+)$
$\therefore$ Profit for 30 apples $=30 \times 8=₹ 240$

Number of pomegranates sold 50
Loss per pomegranate $=₹ 5(-)$
Loss on selling 50 pomegranates $=50 \times(-5)=₹-250$
Overall loss $=-250+240=₹-10$
i.e. loss ₹ 10 .

Question $8 .$
During a drought, the water level in a dam fell 3 inches per week for 6 consecutive weeks. What was the change in the water level in the dam at the end of this period?
Solution:
Water level fall per week $=-3$ inches
$\therefore$ Water level decrease for 6 weeks $=6 ₹(-3)=18$ inches
$\therefore$ decrease of 18 inches of water level.

Question $9 .$
Buddha was born in $563 \mathrm{BC}(\mathrm{BCE})$ and died in $483 \mathrm{BC}(\mathrm{BCE})$. Was he alive in $500 \mathrm{BC}(\mathrm{BCE})$ ?
and find his life time. (Source: Compton's Encyclopedia)
Solution:
Years in $\mathrm{BCC}(\mathrm{BCE})$ are taken as negative integers.
Buddha was bom in $-563$
and died in $-483$
So he was alive in $500 \mathrm{BC}(\mathrm{BCE})$
Life time $=-483-(-563)=-483+563=+80$
Buddha's life time $=80$ years.