Haryana State Board HBSE 8th Class Maths Solutions Chapter 8 Comparing Quantities Ex 8.2 Textbook Exercise Questions and Answers.
Haryana Board 8th Class Maths Solutions Chapter 8 Comparing Quantities Exercise 8.2
Question 1.
A man got a 10% increase in his salary. If his new salary is Rs. 1,54,000, find his original salary.
Solution:
10% increase in salary means
If previous salary is Rs. 100, increased salary = Rs. 110
If new salary is Rs. 110, original salary is Rs. 100
New salary is Rs. 1,54,000, original salary is = \(\frac{100}{110}\) × 154000 = 1,40,000
Original salary = Rs. 1,40,000.
Question 2.
On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the percent decrease in the people visiting the Zoo on Monday.
Solution:
On Sunday Zoo visitor = 845 persons
On Monday Zoo visitor = 169 persons
Decrease in people visiting Zoo on Monday
= 845 – 169 = 676
Percent decrease on Monday
= \(\frac{Decrease}{Visitor on Sunday}\) × 100
= \(\frac{676}{845}\) × 100 = 80%
Question 3.
A shopkeeper buys 80 articles for Rs. 2,400 and sells them for a profit of 16%. Find the selling price of one article.
Solution:
C.P. of all 80 articles = Rs. 2400
16% profit means if C.P. is Rs. 100, S.P. is Rs. 116
Therefore, if C.P. is Rs. 2400,
S P = \(\frac{116}{100}\) × 2400 = 2784
S.P. of 80 articles = Rs. 2784
∴ S.P. of one article = Rs. 34.80.
Question 4.
The cost of an article was Rs. 15,500. Rs. 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.
Solution:
C.P. of article = Rs. 15500
Charge on its repairing = Rs. 450
So, new C.P. = Rs. 15500 + Rs. 450
= 15950
At profit of 15% is sold
So, S.P. = 115% of C.P,
= \(\frac{115}{100}\) × 15950
= 18342.50
∴ S.P. = Rs. 18342.50.
Question 5.
A VCR and TV were bought for Rs. 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole transaction.
Solution:
C.P. ofT.V. = Rs. 8000
C.P. of VCR = Rs. 8000
4% loss on VCR means
If C.P. is Rs. 100, S.P. is Rs. 96
So, if C.P. is 8000, S.P. will be
= \(\frac{96}{100}\) × 8000 = 7680
∴ S.P. of VCR = Rs. 7680
8% profit on TV means
If C.P. is Rs. 100, S.P. is Rs. 108
So if C.P. is Rs. 8000, S.P. will be
\(\frac{108}{100}\) × 8000 = 8640
∴ S.P. of T.V. = Rs. 8640
Overall C.P. of TV and VCR
= 8000 + 8000 = 16,000
Overall S.P. of TV and VCR
= 7680 + 8640 = 16320
∵ Overall S.P. > Overall C.P.
⇒ Profit of Rs. (16320 – 16000)
= Rs. 320.
Question 6.
During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at Rs. 1450 and two shirts marked at Rs. 850 each ?
Solution:
10% discount on marked price (M.P.)
⇒ Article of M.P. Rs. 100, has S.P. = Rs. 90
So, if article of M.P. Rs. 1450 has S.P.
= Rs.\(\frac{90}{100}\) × 1450
= Rs. 1305
and if the article of M.P. 1700 has S.P.
= Rs. \(\frac{90}{100}\) × 1700 = Rs. 1530
Two shirts M.P. = 850 × 2 = Rs. 1700
So customer have to pay for Jeans and two shirts
= Rs. 1305 + Rs. 1530 = Rs. 2835.
Question 7.
A milkman sold two of his buffaloes for Rs. 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss.
[Hint: Find C.P. of each]
Solution:
S.P. of each buffalo = Rs. 20000
5% gain means
⇒ a profit of Rs. 5 on C.P. of Rs. 100
⇒ If S.P. is of Rs. 105, C.P. is Rs. 100
∴ If S.P. is Rs. 20,000
C.P. = Rs. \(\frac{100}{105}\) × 20,000 = 19048
∴ C.P. of one of buffalo = Rs. 19048
10% loss on other buffalo means
If S.P. is 90, C.P. is Rs.. 100
So, if S.P. is Rs. 20,000,
C.P. = Rs. \(\frac{100}{90}\) × 20,000
= Rs. 22222
∴ C.P. of other buffalo = Rs. 22222
∴ Overall S.P. = Rs. 20,000 + Rs. 20000
= Rs. 40,000
Overall C.P. = Rs. 19048 + Rs. 22222
= Rs. 41270
∵ Overall S.P. > Overall C.P.
⇒ Profit of Rs. (41270 – 40000) = Rs. 1270
∴ Net profit = Rs. 1270.
Question 8.
The price of a TV is Rs. 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.
Solution:
Price of TV = Rs. 13,000
Sale tax charge = 12%
∴ Sale tax on T.V.= 12% of Rs. 13,000
= Rs. \(\frac{12}{100}\) × 13000
= Rs. 1560
∴ Amound paid by Vinod for TV
= Rs. 13000 + Rs. 1560
= Rs. 14560.
Question 9.
Arun bought a pair of skates of a sale where the discount given was 20%. If the amount he pays is Rs. 1,600, find the marked price.
Solution:
20% discount means
For M.P. of Rs. 100, S.P.
= Rs. (100 – 20) = Rs. 80
So, if S.P. = Rs. 80, M.P. is Rs. 100
If S.P. = Rs. 1600, M.P. will be Rs. \(\frac{100}{80}\) × 1600
= 2000.
M.P. of skates Rs. 2000.
Question 10.
I purchased a hair-dryer for Rs. 5,400 including 8% VAT. Find the price before VAT was added.
Solution:
8% VAT included means.
Rs. 8 is added to original price of Rs. 100
⇒ If including VAT price is Rs. 108, original price = Rs. 100
So including VAT price is Rs. 5400, original price
= RS \(\frac{100}{108}\) × 5400
= Rs. 5000
∴ Price before VAT = Rs. 5000.