DAV Class 8 Maths Solution Chapter 5 Profit Loss & Discount
DAV School Books Class 8 Maths Solution Chapter 5 profit loss and discount all Question Answer. DAV Class 8 5th chapter profit loss and discount full Chapter explanation by expert teacher.
DAV School Books Class 8 Maths Solution Chapter 5 profit loss and discount:
Worksheet 1
1) By selling a bed sheet for ₹640, a shopkeeper earns a profit of 28%. How much did it cost the shopkeeper?
Ans:
Let the cost price (C.P) be ₹ m.
The gain on the sell is ₹ (640 – m).
∴ gain % = (gain/ c.p) × 100 %
= [(640 – m)/m] × 100%
According to the problem the gain percentage is 28%.
∴ [(640 – m)/m] × 100% = 28%
Or, (640 – m) × 100 = 28m
Or, 64000 – 100m = 28m
Or, 128m = 64000
Or, m = 500
∴ we can see that the cost price of the bed sheet was ₹500.
2) Rajan purchased 250 packets of blades at the rate of ₹8 per packet. He sold 70% of the packets at the rate of ₹11 per packet and remaining packets at the rate of ₹9 per packet. Find his gain per cent.
Ans:
Total cost price (C.P) of the blades is ₹ (250×8) = ₹2000
Number of packets sold at ₹11 per packet is
250×70% = 175
Number of packets sold at ₹9 per packet is
250×30% = 75
So the total selling price (S.P) of blades
= (175×11) + (75×9)
= 1925+675
= 2600
∴ Gain = S.P – C.P = ₹ (2600 – 2000) = ₹600
Gain % = (Gain/C.P)% = (600/2000)×100% = 30%
∴ The total profit earned by Rajan on the sale is 30%.
3) Ankit sold two jeans for ₹990 each. On one he gains 10% and on the other he lost 10%. Find his gain or loss percent in the whole transaction.
Ans:
Ankit sold 2 jeans for ₹990 each so the total selling price
S.P = ₹ (990×2) = ₹1980
C.P of the first jeans = ₹ [990 × (100/110)] = ₹900
C.P of the second jeans = ₹ [990 × (100/90)] = ₹1100
So, the total C.P of two jeans = ₹2000
We can see that the C.P is greater than the S.P which means that Ankit faced loss in the transaction.
∴ Loss = (C.P – S.P) = ₹ (2000 – 1980) = ₹20
∴ Loss % = Loss/ C.P = (20/2000) × 100 % = 1%
[Short trick: If the selling prices of two products are same and one product is sold at a% gain and the other is sold at a% loss then there will be overall loss on the whole transaction.
The loss percentage on the whole transaction will be:
(a2/100)%
For example, in the above problem one product was sold at 10% gain and one product was sold at 10% loss so the overall loss percentage on the whole transaction will be = (102/100) % = 1% ]
4) Nidhi purchased two sarees for ₹2150 each. She sold one saree at a loss of 8% and the other at gain. If she had a gain of Rs.1230 on the whole transaction, find the selling price of the second saree.
Ans:
Nidhi purchased two sarees for ₹2150 each so the cost price (C.P) of both sarees will be ₹ (2×2150) = ₹4300
She had a gain of ₹1230 on the whole transaction so
Total selling price (S.P) = C.P + Gain = ₹ (4300+1230)
= ₹ 5520
Saree 1 is sold at a loss of 8% so the selling price of the saree will be = ₹ 2150× [(100-8)/100]
= ₹ 2150× (92/100) = ₹1978
We know that
Selling price of saree 1 + selling price of saree 2 = selling price of both saree
Or, ₹1978 + selling price of the saree 2 = ₹ 4300
Or, Selling price of the saree 2 = ₹ (4300 – 1978)
∴ Selling price of the saree 2 = ₹ 2322
Therefore we can say that the selling price of the 2nd saree is ₹2322.
5) By selling 35 greeting cards, shopkeeper loses an amount equal to the selling price of 5 greeting cards. Find his loss per cent.
Ans:
Let’s assume that the selling price of one greeting card is ₹1.
∴Selling price of 35 cards is ₹1×35 = ₹35
According to the question the loss is equal to selling price of 5 greeting cards and the selling price of 5 greeting cards is ₹1×5 = ₹5.
So the shopkeeper loses ₹5 selling the cards.
We know that,
Cost price = selling price + loss = ₹35 + ₹5 = ₹40
The loss percent is = (loss/ cost price) × 100%
= (5/40) ×100% = 12.8%
∴ The loss percentage on the total transaction is 12.8%.
6) A man brought bananas at the rate of 10 for ₹15 and sold at the rate of one dozen bananas for ₹15. Find his gain or loss per cent.
Ans:
The cost price of 10 bananas is ₹15.
So the cost price of 1 banana is ₹ (15/10) = ₹1.5
The selling price of 12 bananas is ₹15
So the selling price of 1 banana is ₹ (15/12) = ₹1.25
We can observe from the above that the cost price of one banana is higher than the selling price of a banana. So the man had loss selling the bananas.
Loss = cost price of one banana – selling price of one banana = ₹ (1.5 – 1.25) = ₹0.25.
Loss percentage = (loss/cost price) ×100%
= (0.25/1.5) ×100% = 16.66%
∴ We can say that the man incurred a loss of 16.66%.
Worksheet 2
1) The marked price of a pant is ₹1250 and the shopkeeper allows a discount of 8% on it. Find the discount and the selling price of the pant.
Ans:
Discount on any product always applies on the marked price. The marked price of the pant is ₹1250
And the rate of discount applied on it is 8%.
So the discount is ₹1250×8% = ₹100
∴ The selling price of the pant is = marked price – discount
Selling price = ₹ (1250 – 100) = ₹1150
Therefore the discount is ₹100 and the selling price is ₹1150.
2) The marked price of a water cooler is ₹5400. The shopkeeper offers an off season discount of 20% on it. Find its selling price.
Ans:
The marked price of the water cooler M.P = ₹5400
The rate of discount r = 20%
∴ Discount = M.P × r% = ₹ (5400×20%) = ₹1080
∴ The selling price of the water cooler
S.P = M.P – Discount = ₹ (5400 – 1080) = ₹4320
∴ The selling price of the water cooler is ₹4320.
3) An almirah of marked price ₹4000 is sold for ₹3700 after allowing certain discount. Find the rate of discount.
Ans:
The marked price of the almirah M.P = ₹4000
The selling price of the almirah S.P = ₹3700
∴ Total discount = ₹ (S.P – M.P) = ₹ (4000-3700) = ₹300
The discount percentage
= {(discount/M.P) ×100] %
= [(300/4000) × 100] %
= 7.5%
The rate of discount offered on the almirah is 7.5%
4) Find the rate of discount being given a on a ceiling fan whose selling price is ₹1175 after allowing a discount of ₹75 on its marked price.
Ans:
The selling price of the Ceiling fan S.P = ₹1175
The discount offered on the Ceiling fan = ₹75
∴ The marked price of the Ceiling fan
M.P = ₹ (S.P + Discount) = ₹ (1175 + 75) = ₹1250
∴ The discount percentage
= [(Discount/M.P) × 100] %
= [(75/1250) ×100] %
= 6%
∴ The discount percent offered on the marked price of the ceiling fan is 6%.
5) Find the marked price of a washing machine which is sold at ₹8400 after allowing a discount of 16%.
Ans:
The selling price of the washing machine
S.P = ₹8400
The discount percentage offered on the marked price
r =16%
∴ The marked price of the washing machine
M.P
= S.P× [1/(1-r%)]
= S.P× [100/(100-r)]
= ₹8400× (100/84)
= ₹10000
∴ The marked price of the washing machine is ₹10000.
6) A dinner set was bought for ₹2464 after getting a discount of 12% on its marked price. Find the marked price of the dinner set.
Ans:
The selling price of the dinner set
S.P = ₹2464
The discount percentage offered on the marked price
r =12%
The marked price of the dinner set = M.P
∴ M.P
= S.P×[1/(1-r%)]
= S.P× [100/(100-r)]
= ₹2464× [100/ (100-12)]
= ₹2464× (100/88)
= ₹2800
∴ The marked price of the dinner set is ₹2800.
7) The marked price of a computer is ₹22000. After allowing a 10% discount, a dealer still makes a profit of 20%. Find the cost price of a computer?
Ans:
The marked price of a computer is
M.P = ₹22000
The discount percentage offered on the M.P of the computer is r = 10%
∴ The discount offered is = M.P× 10% = ₹22000×10%
= ₹2200
∴ The selling price S.P = M.P – Discount
= ₹ (22000 – 2200) = ₹19800
According to the question the dealer makes 20% profit on the transaction.
Profits are usually calculated based on the cost price of the product.
According to the problem,
Cost price = C.P
Profit percentage = p% = 20%
Selling price = S.P = ₹19800
We know that,
C.P + C.P × p% = S.P
Or, C.P× [1+(p/100)] = S.P
Or, C.P× [1+(20/100)] = 19800
Or, C.P = 19800/ [1+(20/100)]
Or, C.P = 19800×100/120
Or, C.P = 16500
∴ The cost price of the computer is ₹16500.
8) The marked price of a double bed is ₹9575. A shopkeeper allows a discount of 12% on its marked price and still gains 10%. Find the cost price of the double bed.
Ans:
The marked price of the double bed is
M.P = ₹9575
The discount percentage offered on the M.P of the double bed is r = 12%
∴ The discount offered is = M.P× 12% = ₹9575×12%
= ₹1149
∴ The selling price S.P = M.P – Discount
= ₹ (9575 – 1149) = ₹8426
According to the question the shopkeeper makes 10% profit on the transaction.
Profits are usually calculated based on the cost price of the product.
According to the problem,
Cost price = C.P
Profit percentage = p% = 10%
Selling price = S.P = ₹8426
We know that,
C.P + C.P × p% = S.P
Or, C.P× [1+ (p/100)] = S.P
Or, C.P× [1+ (10/100)] = 8426
Or, C.P = 8426/ [1+ (10/100)]
Or, C.P = 8426×100/110
Or, C.P = 7660
∴ The cost price of the double bed is ₹7660.
9) How much a shopkeeper must mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%, if the cost price of the goods is ₹20000?
Ans:
According to the question the cost price of the goods is C.P = ₹20000.
The profit percentage = p% = 20%
So, the selling price of the goods will be
∴ S.P = C.P + C.P × p%
Or, S.P = C.P× [1+ (p/100)]
Or, S.P = 20000× [1+ (20/100)]
Or, S.P = 20000× 6/5
Or, S.P = 24000
Now, the selling price S.P = 24000
Discount percentage r% = 25%
And Marked price = M.P
∴ M.P = S.P/[1 – (r%)]
Or, M.P = 24000/ [1 – (25/100)]
Or, M.P = 24000×100/75
Or, M.P = 32000
Now we know that
C.P = ₹20000
M.P = ₹32000
Mark up = ₹ (32000-20000) = ₹12000
∴ Markup percentage = (markup/C.P)×100 %
Or, Markup percentage = (12000/20000) ×100 %
Or, Markup percentage = 60%
Therefore, the shopkeeper has to markup his goods by 60% which turns out to be ₹12000 to gain a 20% profit even after a discount of 25%.
10) Priti allows 8% discount on the marked price of the suits and still makes a profit of 15%. If her gain over the sale of a suite is ₹156 then find the marked price of the suit.
Ans:
The cost price of the suit is C.P.
The profit percent earned by Priti is 15%
The profit earned in the whole transaction is ₹156
∴ C.P×15% = 156
Or, C.P = 156/15%
Or, C.P = 1040
We can see that the C.P is ₹1040.
The profit earned is ₹156
∴ The selling price S.P = ₹ (1040+156) = ₹1196
The marked price = M.P
The discount offered on the marked price = r% = 8%
∴ M.P – M.P × r% = S.P
Or, M.P× [1- r%] = S.P
Or, M.P× [1- 8%] = 1196
Or, M.P = 1196/(1-8%)
Or, M.P = 1196× (100/92)
Or, M.P = 1300
Therefore, the marked price of the suite is ₹1300.
Worksheet 3
1) Rehana purchased a dress for ₹5400 including 8% VAT. Find the price of the dress before VAT was added.
Ans:
Rehana purchased the dress for ₹5400 including VAT which is 8%.
∴ VAT amount = ₹5400× (8/100) = ₹432
Therefore, the price of the dress before adding VAT = ₹ (5400 – 432) = ₹4968
The cost of the dress before adding VAT will be ₹4968.
2) What will be the amount one has to pay for the following items if 5% VAT is added to their price?
i) A bottle of hair styling gel at ₹185.
ii) A laptop at ₹55,000.
iii) A mobile at ₹36,200.
Ans:
i) Cost of a bottle of hair styling gel = ₹185
VAT charged = 5%
VAT amount = ₹185×5/100 = ₹9.25
The amount one has to pay to buy a bottle of hair styling gel = ₹ (185+9.25) = ₹194.25
ii) Cost of a laptop = ₹55000
VAT charged = 5%
VAT amount = ₹55000×5/100 = ₹2750
The amount one has to pay to buy a laptop = ₹ (55000+2750) = ₹57750
iii) Cost of a mobile = ₹36200
VAT charged = 5%
VAT amount = ₹36200×5/100 = ₹1810
The amount one has to pay to buy mobile = ₹ (36200+1810) = ₹38010
3) Raman purchased a music system at ₹ 48,000 including VAT. If the cost price of the music system was ₹40,000, what is the VAT (in %) has he paid?
Ans:
The cost price of the music system = ₹40000
The amount paid by Raman for the music system= ₹48000
The VAT amount = ₹ (48000 – 40000) = ₹8000
The VAT percentage = [(8000/40000) ×100] % = 20%
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