profit and loss chapter in math
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Answer:
Access Answers to RS Aggarwal Solutions for Class 8 Maths Chapter 10 – Profit and Loss
Exercise 10A
Q1.Find the gain or loss percent when:
i CP = ₹620 and SP = ₹713
Solution: we know that SP is more than CP so it’s a gain.As the formula states Gain = SP – CP713 – 620 = 93
Gain% = (Gain × 100) / CP
= (93 × 100) / 620
= 15%
ii CP = ₹675 and SP = ₹630
Solution: we know that SP is less than CP so it’s a loss.As the formula states Loss = CP – SP675 – 630 = 45
Loss% = (Loss × 100) / CP
= (45 × 100) / 675
= 6.66%
iii CP = ₹345 and SP = ₹372.60
Solution: we know that SP is more than CP so it’s a gain.As the formula states Gain = SP – CP372.60 – 345 = 27.60
Gain% = (Gain × 100) / CP
= (27.60 × 100) / 345
= 8%
iv CP = ₹80 and SP = ₹76.80
Solution: we know that SP is less than CP so it’s a loss.As the formula states Loss = CP – SP80 – 76.80 = 3.20
Loss% = (Loss × 100) / CP
= (3.20 × 100) / 80
= 4%
Q2.Find the selling price when:
i CP = ₹1650 and Gain = 4%
Solution: As the formula states SP = ((100 + Gain %) /100) × CP= ((100+4)/100) × 1650= (104/100) × 1650
=1716
∴ The selling price is 1716
ii CP = ₹915 and Gain = 623%
Solution: As the formula states SP = ((100 + Gain %) /100) × CP= ((100+(20/3))/100) × 915= ((320/3)/100) × 915
=976
∴ The selling price is 976
iii CP = ₹875 and Loss = 12%
Solution: As the formula states SP = ((100 – Loss %) /100) × CP= ((100 – 12)/100) × 875= (88/100) × 875
=770
∴ The selling price is 770
iv CP = ₹645 and Loss = 1313%
Solution: As the formula states SP = ((100 – Loss %) /100) × CP= ((100-(40/3))/100) × 645= ((260/3)/100) × 645
= (260/300) × 645
=559
∴ The selling price is 559
Q3.Find the cost price when:
i SP = ₹1596 and Gain = 12%
Solution: As the formula states CP = (100 / (100+ Gain %)) × SP= (100/ (100+12)) × 1596= (100/112) × 1596
=1425
∴ The cost price is 1425
ii SP = ₹2431 and Loss = 6 ½ %
Solution: As the formula states CP = (100 / (100 – Loss %)) × SP= (100/ (100-(13/2))) × 2431= (100/ (187/2)) × 2431
= (200/187) × 2431
=2600
∴ The cost price is 2600
iii SP = ₹657.60 and Loss = 4%
Solution: As the formula states CP = (100 / (100 – Loss %)) × SP= (100/ (100-4)) × 657.60= (100/96) × 657.60
=658
∴ the cost price is 658
iv SP = ₹34.40 and Gain = 7 ½ %
Solution: As the formula states CP = (100 / (100+ Gain %)) × SP= (100/ (100+ (15/2))) × 34.40= (100/ (215/2)) × 34.40
= (200/215) × 34.40
=32
∴ the cost price is 32
Q4. Manjit bought an iron safe for ₹12160 and paid ₹340 for its transportation. Then, he sold it for ₹12875. Find his gain percent.
Solution: Lets solve by using, the total cost of iron safe = purchase cost + transportation
= 12160 + 340 = 12500
CP of iron safe = 12500
SP of iron safe = 12875
Since, SP is more than CP so it’s a gain.
Gain = SP – CP = 12875 – 12500 = 375
Gain % = (Gain × 100) / CP
= (375 × 100) / 12500
= 3%
∴ The Gain percent is 3%
Q5. Robin purchased an old car for ₹73500. He spent ₹10300 on repairs and paid ₹2600 for its insurance. Then he sold it to a mechanic for ₹84240. What was his percentage gain or loss? Hint: overheads =₹10300+₹2600= ₹12900
Solution: We know that,
Actual price of old car= purchase price + overheads
=73500 + 12900
=86400
∴ the CP =₹86400
SP = ₹84240
Since, SP is less than CP so it’s a loss.
Loss = CP – SP
=86400 – 84240
= 2160
Loss% = (Loss × 100) / CP
= (2160 × 100) / 86400
= 2.5%
∴ The Loss percent is 2.5%
Q6.Hari bought 20kg of rice at ₹36 per kg and 25kg of rice at ₹32 per kg. He mixed the two varieties and sold the mixture at ₹38 per kg. Find his gain percent in the whole transaction.
Solution: We know that,
Total weight of rice = 20 + 25 = 45
So, total cost of both varieties = (20×36) + (25×32) = 720 + 800 = 1520
∴ The CP =₹1520
SP = weight × Rate = 45×38 = 1710
Since, SP is more than CP so it’s a gain.
Gain = SP – CP = 1710 – 1520 = ₹190
Gain % = (Gain × 100) / CP
= (190 × 100) / 1520
= 12.5%
∴ The Gain percent is 12.5%
Q7. Coffee costing ₹250 per kg was mixed with chicory costing ₹75 per kg in the ratio 5:2 for a certain blend. If the mixture was sold at ₹230 per kg, find the gain or loss percent. Hint: let 5kg of coffee be mixed with 2kg of chicory
Solution: Let us consider x as the common multiple
Cost of 5kg of coffee= 5x = 5 × 250 = ₹1250
Cost of 2kg of coffee= 2x = 2 × 75 = ₹150
∴ the cost of the mixture is 5x + 2x = 1250 + 150
7x = 1400
x = 1400/7 = 200
So, CP of mixture = 200
SP of mixture = 230
Since, SP is more than CP so it’s a gain.
Gain = SP – CP = 230 – 200 = ₹30
Gain % = (Gain × 100) / CP
= (30 × 100) / 200
= 15%
∴ The Gain percent is 15%