Exercise 4.2 - Chapter 4 Life Mathematics 8th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex $4.2$
Question 1.
Fill in the blanks:
(i) Loss or gain percentage is always calculated on the
Answer:
Cost Price
(ii) A mobile phone is sold for $₹ 8400$ at a gain of $20 \%$. The cost price of the mobile phone is
Answer: $₹ 7000$ Hint:
Let cost price of mobile be $₹ x$
Given that selling price is $₹ 8400$ and gain is $20 \%$
As per formula,
$\mathrm{SP}=\frac{(100+\text { gain } \%)}{100} \times \mathrm{CP}$
$\therefore$ by substituting we get,
$\begin{aligned}
8400 &=\frac{(100+20)}{100} \times x \\
8400 &=\frac{120}{100} x \\
x &=\frac{8400 \times 100}{120}=₹ 7000
\end{aligned}$
(iii) An article is sold for ₹ 555 at a loss of $7 \frac{1}{2} \%$. The cost price of the article is
Answer:

₹ 600

(iv) A mixer grinder marked at $₹ 4500$ is sold for $₹ 4140$ after discount. The rate of discount is
Answer:
$8 \%$

(v) The total bill amount of a shirt costing ₹ 575 and a T-shirt costing ₹ 325 with GST of $5 \%$ is
Answer:
Cost of price shirt = ₹ 575 (CP)
GST $=5 \%$
Bill amount formula $=\mathrm{CP} \times\left(\frac{100+\mathrm{GST} \%}{100}\right)$
$=575 \times\left(\frac{100+5}{100}\right)=575 \times \frac{105}{100}=₹ 603.75$
Cost of price shirt $=₹ 325$ (CP)
GST $=5 \%$
Bill amount $=\mathrm{CP} \times\left(\frac{100+\mathrm{GST} \%}{100}\right)$
$=325 \times\left(\frac{100+5}{100}\right)=₹ 341.25$
$\therefore$ Total bill amount $=₹ 603.75+₹ 341.25=₹ 945$
 

Question $2 .$
If selling an article for $₹ 820$ causes $10 \%$ loss on the selling price, then find its cost price.
Answer:
Given that selling price (SP) $=₹ 820$
Loss $\%=10 \%$

$\begin{aligned}
\text { As per formula SP } &=\mathrm{CP} \times \frac{(100-\text { loss } \%)}{100} \\
\therefore \text { Substituting in formula, we get } \\
820 &=\mathrm{CP} \times\left(\frac{100-10}{100}\right) \\
\therefore \mathrm{CP} &=\frac{82 \varnothing \times 100}{90}=911
\end{aligned}$

Question $3 .$
If the profit earned on selling an article for ₹ 810 is the same as loss on selling it for ₹ 530 , then find the cost price of the article.
Answer:
Case 1: Profit = Selling price $(\mathrm{SP})-$ Cost price $(\mathrm{CP})$
Case 2: Loss = Cost price (CP) - Selling price (SP)
Given that profit of case $1=$ loss of case 2
$\begin{aligned}
&\therefore \mathrm{P}=810-\mathrm{CP} \\
&\mathrm{L}=\mathrm{CP}-530 \\
&\text { Since profit }(\mathrm{P})=\text { loss }(\mathrm{L}) \\
&810-\mathrm{CP}=\mathrm{CP}-530 \\
&\therefore 2 \mathrm{CP}=810+530=1340 \Rightarrow \mathrm{C} \cdot \mathrm{P}=\frac{1340}{2} \\
&\therefore \mathrm{CP}=670
\end{aligned}$

Question $4 .$
If the selling price of 10 rulers is the same as the cost price of 15 rulers, then find the profit percentage.
Answer:
Let cost price of one ruler be $x$
Given that selling price (SP) of 10 rulers.
i.e., same as cost price (CP) of 15 rulers
$\therefore$ SP of 10 rulers $=15 \times x=15 x$

$\therefore$ Gain $=$ SP of 1 ruler $-$ CP of 1 ruler $=1.5 x-x=0.5 x$
Gain $\%=\frac{\text { Gain }}{\text { CP }} \times 100=\frac{0.5 \not x}{\not} \times 100=50 \%$
 

Question $5 .$
Some articles are bought at 2 for $₹ 15$ and sold at 3 for $₹ 25$. Find the gain percentage.
Answer:
Let cost price of one article be C.P
Given that 2 are bought for $₹ 15$
$\therefore 2 \times \mathrm{CP}=15 \Rightarrow \mathrm{CP}=\frac{15}{2}$
Let selling price of one article be SP
Given that 3 are sold for $₹ 25$
$\begin{aligned}
&\therefore 3 \times \mathrm{SP}=25 \Rightarrow \mathrm{SP}=\frac{25}{3} \\
&\therefore \text { Gain }=\mathrm{SP}-\mathrm{CP}=\frac{25}{3}-\frac{15}{2}=\frac{50-45}{6}=\frac{5}{6}
\end{aligned}$
Gain $\%=\frac{\text { Gain }}{\text { CP }} \times 100=\frac{\frac{5}{6}}{\frac{15}{2}} \times 100=\frac{\not 8}{6{ }_{3}} \times \frac{\not 2}{15_{3}} \times 100=\frac{100}{9}$ $=11 \frac{1}{9}$
 

Question $6 .$
By selling a speaker for $₹ 768$, a man loses $20 \%$. In order to gain $20 \%$, how much should he sell the speaker?

Answer:
Selling price (SP) of speaker $=₹ 768$
Loss \% $=20 \%$
as per formula
$\mathrm{SP}=\mathrm{CP} \times \frac{(100-\operatorname{loss} \%)}{100}$
$\therefore 768=C P \times\left(\frac{100-20}{100}\right)$
$\therefore \mathrm{CP}=\frac{768 \times 100}{80}=960$
For gain of $20 \%$, we should now calculate the selling price
$\begin{aligned}
\therefore \mathrm{SP} &=\mathrm{CP}\left(\frac{100+\text { gain } \%}{100}\right) \\
&=960\left(\frac{100+20}{100}\right)=960 \times \frac{120}{100} \\
=96 \times 12 &=₹ 1152
\end{aligned}$

Question 7.
Find the unknowns $x, y$ and $z$.

Answer:
(i) Book marked price $=₹ 225$ discount $8 \%$
$\therefore$ Selling price $(\mathrm{x})=$ Marked price $\times\left(\frac{(100-d \%)}{100}\right)$
$=225 \times \frac{(100-8)}{100}=225 \times \frac{92}{100}=₹ 207$
(ii) LED TV selling price $=11970$ discount $=5 \%$, Marked price $=y$
$\therefore$ Selling price Marked price $\mathrm{y} \times\left(\frac{(100-d \%)}{100}\right)$
$\therefore 11970=\mathrm{y} \times \frac{(100-5)}{100}$
$\therefore y=\frac{11970 \times 100}{95}=126 \times 100=₹ 12,600$
(iii) Digital clock marked price (MP) $=₹ 750, \mathrm{MP}=₹ 12.600$
Selling price (SP) $=₹ 615$, Discount $=\mathrm{z}$
$\begin{array}{r}
\mathrm{SP}=\mathrm{MP} \times\left(\frac{(100-d \%)}{100}\right) \\
\therefore 615=750 \times \frac{(100-z)}{100} \\
\therefore(100-\mathrm{z})=\frac{615 \times 100}{750} \\
100-\mathrm{z}=82 \\
\therefore \mathrm{z}=100-82, \text { Discount }=18 \%
\end{array}$

Question 8.
Find the total bill amount for the data given below:

Answer:
Formula for discounted price LW = Marked price (MP) $\times \frac{(100-d \%)}{100}$
When $\mathrm{d}$ is the discount $\%$
(i)
$\therefore \mathrm{DP}=\mathrm{MP} \times\left(\frac{(100-d \%)}{100}\right)$
School bag $=\operatorname{MP} \times\left(\frac{(100-d \%)}{100}\right)$
$=500 \times \frac{(100-5)}{100}=\frac{500 \times 0.95}{100}=₹ 475$
$\begin{aligned}
\text { Hair drier } &=\mathrm{MP} \times\left(\frac{(100-d \%)}{100}\right) \\
&=2000 \times\left(\frac{(100-10)}{100}\right)=2000 \times 0.9=₹ 1,800 .
\end{aligned}$
For bill amount, we should apply GST on the discounted value of the items.
Formula: Bill amount $=$ Discounted price $\times\left(\frac{(100+\mathrm{GST} \%)}{100}\right)$
$\therefore$ For (i) School bag.
Bill amount $475 \times\left(\frac{(100+12)}{100}\right)=475 \times 1.12=\%$ '532

$\therefore$ For (ii) Hair drier,
Bill amount $=1800 \times\left(\frac{(100+28)}{100}\right)=1800 \times 1.28=$
$\therefore$ Total bill amount Bill amount of School bag + Stationary + Cosmetics + Hair drier $=532+252+1357+2304$
$=₹ 4.445$

Question $9 .$
A branded Air-Conditioner (AC) has a marked price of ₹ 38000 . There are 2 options given for the customer.
(i) Selling Price is the same ₹ 38000 but with attractive gifts worth ₹ 3000
(or)
(ii) Discount of $8 \%$ on the marked price but no free gifts. Which offer is better?
Answer:
Marked price of $\mathrm{AC}=₹ 38,000$
Option 1:
Selling price $=₹ 38000$ \& gifts worth ₹ 3000
$\therefore$ Net gain for customer $=₹ 3000$ as there is no discount on AC
Option 2:
Discount of $8 \%$, but no gift
$\therefore$ Discounted value $=\mathrm{MP} \times\left(\frac{(100-d \%)}{100}\right)$
$38000 \times \frac{(100-8)}{100}=38000 \times 0.92=34960$
$\therefore$ Savings for customer $=38000-34960=3040$
Therefore, the customer gets 3000 gift in option I where as he is able to save only ₹ 3040 in option 2 . Therefore, option 2 is better.
 

Question 10 .
If a mattress is marked for $₹ 7500$ and is available at two successive discount of $10 \%$ and $20 \%$, find the amount to be paid by the customer.
Answer:
Marked price of mattress $=₹ 7500$

Discount $d_{1}=10 \%$
Discount $d_{2}=20 \%$
$\begin{aligned}
\text { Price after discount } d_{1} &=\mathrm{MP} \times \frac{\left(100-d_{1} \%\right)}{100} \\
&=7500 \times \frac{(100-10)}{100}=7500 \times \frac{90}{100}=6750 \\
\text { Price after second discount } d_{2} &=\text { Discount price } \times \frac{\left(100-d_{2} \%\right)}{100} \\
&=6750 \times \frac{(100-20)}{100}=₹ 5400
\end{aligned}$

Objective Type Questions
Question 11 .
A fruit vendor sells fruits for $₹ 200$ gaining $₹ 40$. His gain percentage is
(A) $20 \%$
(B) $22 \%$
(C) $25 \%$
(D) 16

Auswer:
(C) $25 \%$
Hint:
Selling price ₹ 200
Gain $=40$
$\therefore \mathrm{CP}$ - Selling price $-$ gain $=200-40=160$
Gain $\%=\frac{\text { Gain }}{\text { CP }} \times 100=\frac{40}{160} \times 100=25 \%$

Question $12 .$
By selling a flower pot for $\mathrm{Z} 528$, a woman gains $20 \%$. At what price should she sell it to gain $25 \%$ ?
(A) ₹ 500
(B) ₹ 550
(C) ₹ 553
(D) ₹ 573
Answer:
(B) ₹ 550

Question $13 .$
A man buys an article for $₹ 150$ and makes overhead expenses which are $12 \%$ of the cost price. At what price must he sell it to gain $5 \%$ ?
(A) ₹ 180
(B) ₹ 168
(C) ₹ $176.40$
(D) ₹ $88.20$
Answer:
(C) ₹ $176.40$

Question 14.
What is the marked price of a hat which is bought for $\mathrm{Z} 210$ at $16 \%$ discount?
(A) ₹ 243
(B) ₹ 176
(C) ₹ 230
(D) ₹ 250
Answer:
(D) ₹ 250

Question $15 .$
The single discount in \% which is equivalent to two successive discounts of $20 \%$ and $25 \%$ is
(A) $40 \%$
(B) $45 \%$
(C) $5 \%$
(D) $22.5 \%$
Answer:
(A) $40 \%$