8th Maths 8.2

Chapter 8

Comparing Quantities

NCERT Class 8th Solution of Exercise 8.1

NCERT Class 8th Solution of Exercies 8.3

EXERCISE 8.2

1. A man got a 10% increase in his salary. If his new salary is ₹ 1,54,000, find his original salary.

`text{Solution:}`

`text{salary increase 10%}`

`text{new salary ₹ 154000}`

`text{original salary}=(text{new salary}times 100)/(100+text{increase}%)`

`=(154000times100)/(100+10)`

`=(15400000)/(110)`

`= ₹ 140000`

`text{Answer:}`

`text{His original salary was ₹ 140000.}`

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?

`text{Solution:}`

`text{No. of people decrease = Sunday - Monday}`

`=845-169`

`=676`

`text{Decrease percent}`

`=(text{No. of people decrease})/(text{No of people visit on Sunday})times 100`

`=676/845times100`

`=80%`

`text{Answer:}`

`text{Decrease percent 80%.}`

3. A shopkeeper buys 80 articles for ₹ 2,400 and sells them for a profit of 16%. Find the selling price of one article.

`text{Solution:}`

`text{Cost price of 1 article}=2400/80=30`

`text{Profit 16%}`

`text{Selling price =?}`

`text{SP}=(text{CP}(100+text{Profit}))/100`

`=(30(100+16))/100`

`=(30times116)/100`

`=34.80`

`text{Answer:}`

`text{The SP of an article is ₹ 34.80.}`

4. The cost of an article was ₹ 15,500. ₹.450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.

`text{Solution:}`

`text{Cost price ₹ 15500}`

`text{Repair cost   ₹ 450}`

`text{Actual cost  15500 + 450 = 15950}`

`text{Profit = 15%}`

`text{Selling Price = ?}`

`text{SP}= (text{CP}(100+text{Profit}))/100`

`=(15950(100+15))/100`

`=(15950times115)/100`

`=1834250/100`

`=18342.50`

`text{Answer:}`

`text{The selling price of the article is ₹ 18342.50.}`

5. A VCR and TV were bought for ₹ 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.

`text{Solution:}`

`text{For VCR}`

`text{CP ₹ 8000}`

`text{Loss 4%}`

`text{SP = ?}`

`text{SP} = (text{CP}(100-text{Loss}))/100`

`=(8000(100-4))/100`

`=(8000times96)/100`

`=7680`

`text{For TV}`

`text{CP ₹ 8000}`

`text{Profit 8%}`

`text{SP = ?}`

`text{SP} = (text{CP}(100+text{Profit}))/100`

`=(8000(100+8))/100`

`=(8000times108)/100`

`=8640`

`text{Total CP = 8000+8000=16000}`

`text{Total SP = 7680+8640=16320}`

`text{SP}gt text{CP}text{ hence Profit}`

`text{Profit = SP-CP}`

`text{Profit = 16320-16000 = 320}`

`text{Profit%} = (text{Profit}times100)/(text{CP})`

`=(320times100)/16000`

`=2%`

`text{Answer:}`

`text{2% gain in the whole transaction.}`

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 1450 and two shirts marked at 850 each?

`text{Solution:}`

`text{Marked Price of jeans ₹ 1450}`

`text{Marked Price of shirts 2}``times850 = ₹ 1700`

`text{Total Marked Price = 1450 + 1700 = ₹ 3150}`

`text{Discount 10%}`

`text{SP = ?}`

`text{SP}=(text{MP}(100-text{Discount}))/100`

`=(3150(100-10))/100`

`=(3150times90)/100`

`=2835`

`text{Answer:}`

`text{Customer have to pay ₹ 2835.}`

7. J. A milkman sold two of his buffaloes for ₹ 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 CP of each)

`text{Solution:}`

`text{First Buffalo}`

`text{SP = ₹ 20000}`

`text{Gain 5%}`

`text{CP = ?}`

`text{CP}=(text{SP}times100)/(100+text{gain})`

`=(20000times100)/(100+5)`

`=2000000/105`

`=400000/21`

`=19047.62`

`text{Second Buffalo}`

`text{SP = ₹ 20000}`

`text{Loss 10%}`

`text{CP = ?}`

`text{CP}=(text{SP}times100)/(100-text{loss})`

`=(20000times100)/(100-10)`

`=2000000/90`

`=200000/9`

`=22222.22`

`text{Total CP} = 19047.62+22222.22``=41269.84`

`text{Total SP} = 20000 + 20000`` = 40000`

`text{CP}gt text{SP hence Loss}`

`text{Loss = CP - SP}`

`=41269.84 - 40000`

`=1269.84`

`text{Answer:}`

`text{Overall loss is ₹ 1269.84.}`

8. The price of a TV is 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.

`text{Solution:}`

`text{MP = 13000}`

`text{Sales tax = 12%}`

`text{CP = ?}`

`text{CP}=(text{MP}(100+text{ST}))/100`

`=(13000(100+12))/100`

`=(13000times112)/100`

`=14560`

`text{Answer:}`

`text{Vinod have to pay ₹ 14560.}`

9. Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1,600, find the marked price.

`text{Solution:}`

`text{Discount 20%}`

`text{CP = ₹ 1600}`

`text{MP = ?}`

`text{MP}=(text{CP}times100)/(100-text{Discount})`

`=(1600times100)/(100-20)`

`=(1600times100)/80`

`=2000`

`text{Answer:}`

`text{The Marked price ₹ 2000.}`

10. I purchased a hair dryer for ₹ 5,400 including 8% VAT. Find the price before VAT was added.

`text{Solution:}`

`text{SP = 5400}`

`text{VAT = 8%}`

`text{CP = ?}`

`text{CP}=(text{SP}times100)/(100+text{VAT})`

`=(5400times100)/(100+8)`

`=(5400times100)/108`

`=5000`

`text{Answer:}`

`text{The price before VAT is ₹ 5000.}`

11. An article was purchased for ₹ 1239 including GST of 18%. Find the price of the article before GST was added?

`text{Solution:}`

`text{SP = 1239}`

`text{GST = 18%}`

`text{CP = ?}`

`text{CP}=(text{SP}times100)/(100+text{GST})`

`=(1239times100)/(100+18)`

`=(1239times100)/118`

`=1050`

`text{Answer:}`

`text{The price before GST ₹ 1050.}`