PROFIT,LOSS AND DISCOUNT
EXERCISE 8 (A)
QUESTION 1
A peon purchased a chair for ₹ 700, spent ₹ 170 on its repair and ₹ 30 on the cartage.If he sold the chair for ₹ 1080, what is his gain percent ?
Sol :
Cost price of chair = 700 + 170 + 30
= 900
Selling price of chair = 1080
Gain = Cost price – Selling price
= 1080 – 900
= 180
Gain Percent
= 20 %
QUESTION 2
Ramesh bought 10 cycles for ₹ 500 each.He spent ₹ 2000 on the repair of all the cycles.He sold five of them for ₹ 750 each and the remaining for ₹ 550 each.What is total gain or loss %?
Sol :
Cost price of 1 cycle = 500 ₹
Cost price of 10 cycle = 500 × 10
= 5000 ₹
Total spending on repair = 2000 ₹
Total cost price = 5000 ₹ + 2000 ₹
= 7000 ₹
Selling price of 5 cycles for ₹ 750 = 5 × 750
= 3750 ₹
Selling price of 5 cycles for ₹ 550 = 5 × 550
= 2750 ₹
Selling price of 10 cycles = S.P of 5 cycles for 750 + S.P of 5 cycles for 550
= 3750 + 2750
= 6500 ₹
Loss = Cost price – Selling price
= 7000 – 6500
= 500 ₹
Loss percentage
QUESTION 3
By selling an article for ₹ 960 a man incurr a loss of 4%.What was the cost price of the article?
Sol :
Cost price of article
= 1000
QUESTION 4
If the selling price of 20 articles is equal to the cost price of 15 articles, then what is the loss percentage ?
Sol :
Given that, a = 20 and b = 15
According to the formula,
Profit %
%
QUESTION 5
A hawker gains the selling price of 4 ball-point pens on selling 1 dozen pens.What is his gain percentage?
Sol :
As we know 1 dozen = 12 pens
Let the selling price of of one ball point pen be x then the profit will be equal to 4x
And the selling price of 12 pens = 12 x
Then cost price of 12 pens is equals to (C.P = S.P – profit)
Cost price of 12 pens = Selling price – Profit
C.P = 12x – 4x
C.P = 8x
Then ,
= 33.33 %
QUESTION 6
A man bought pencils at the rate of 6 for ₹ 4 and sold them at the rate of 4 for ₹ 6. What is his gain percentage in transaction?
Sol :
6 pencils are bought for ₹ 4
So, 1 is bought for
4 are sold for ₹ 6
So, 1 is sold for
Here, S.P > C.P , so , it is a gain
gain = S.P – C.P = 1.5 – 0.66 = ₹ 0.84
∴ gain percent
= 127%
QUESTION 7
By selling a basket of mangoes for ₹ 105, a fruit seller loses 30%. For how much should he sell it to gain 40%?
Sol :
As we know
….(i)
And here we know S.P = 105 ,
Loss % = 30 % and putting these in (i)
C.P = 150
Gain % = 40 and putting these two in (ii) , we get
…..(ii)
S.P = 14 × 15
S.P = 210
QUESTION 8
A man sold a book at a loss of 20%.If he had sold the books for ₹ 12 more, he would have gained 10% .Find the cost price of the book.
Sol :
We know that
Loss % = 20 % and in this case let the Selling Price be x
Putting these in (i)
…..(i)
…(ii)
…(iii)
And here we know gain % = 10 % , in this case we have Selling Price = x + 12
Putting these two in (iii) we get
…(iv)
From (ii) and (iv) , we get
Which means
3x = 12 × 8
x = 32 …(v)
putting (v) in (ii)
C.P = 40
QUESTION 9
A trader sells two cycles at ₹ 1188 each, gaining 10% on the first cycle and losing 10% on the second cycle.What is the profit or loss percentage in the whole transaction ?
Sol :
Case 1 (First cycle)
C.P = 1080
Case 2 (Second cycle)
C.P = 1320
S.P = 1188 + 1188
S.P = 2376
C.P = 1080 + 1320
C.P = 2400
Here , we come to know that S.P < C.P . So , it is a loss
Loss = C.P – S.P
Loss = 2400 – 2376
Loss = 24
Loss % = 1 %
QUESTION 10
A merchant bought two calculator which together cost him ₹ 4800.He sold one of them at a loss 15% and the other at a gain of 19%.If the selling price of both the calculator is equal, find the cost price of the lower priced calculator.
Sol :
Let the S.P. be x
We know that
also
C.P. of 1st calculator
C.P. of 2nd calculator
Now , C.P. of 1st calculator + C.P. of 2nd calculator = Total cost
x = 2380
C.P. Of 1st calculator = 2800
C.P. of 2nd calculator = 2000
C.P. of lower priced calculator = Rs. 2000
QUESTION 11
A manufacturer sells an article to a wholesale dealer at a profit of 10%.The wholesale dealer sells it to a shopkeeper at 20% profit.The shopkeeper sells it to the customer for ₹ 56,100 at a loss of 15%.What is the cost price of the article to the manufacturer?
Sol :
Given : Selling price of article = 56,100 and at loss of 15 %
We know that
Cost price of article for shopkeeper = 66,000 (Shopkeeper’s cost price)
Now , lets find C.P of article for the wholesale dealer . In this case S.P = 66000 and at a gain of 20 %
= 55000
Now , lets find C.P of article for manufacturer . In this case S.P = 55000 and at a gain of 10 %
= 50000
Cost price of the article to the manufacturer = 50,000
QUESTION 12
A man buys a plot of agricultural land for ₹ 3,60,000. He sells one third of it at a loss of 20% and two fifth at a gain of 20%.At what price must he sell the remaining field so as to make an overall profit of 10% ?
Sol :
C.P = 360000
To gain 10% on wholeland ,
S.P = 360000 + 10% of 360000
= 396000
of the land sold on 20% loss
S.P of land
= 96000
S.P of of the land
= 180000
Thus , S.P of the remaining land
= 39600 – 96000 – 180000
= 120000
ALTERNATE METHOD
S.P of total agricultural field at a profit of 10%
= 396000
So , S.P of of field
= 96000
S.P of of the field
= 180000
Hence ,
S.P of the remaining field
= 396000-96000-180000
= 120000
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