1. A man got a 10% increase in his salary. If his new salary is ₹1,54,000, find his original salary.
Solution:
Let us assume the original salary be x
Given, the new salary is ₹1,54,000
So,
Original salary + Increment = New salary
Given, the increment is 10% of the original salary
Now,
(x + 10/100 × x) = 154000
x + x/10 = 154000
11x/10 = 154000
x = 154000 × 10/11
= 140000
Hence, the original salary was ₹1,40,000.
2. On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the per cent decrease in the people visiting the zoo on Monday?
Solution:
Given,
Total number of people went to zoo on Sunday = 845
Total number of people went to zoo on Monday = 169
So,
Decrease in the number of people = 845 – 169 = 676
Thus,
Percentage decrease = (Decrease in the number of people/Number of people who went to zoo on Sunday) x 100%
= (676/845 x 100)%
= 80%
Hence, required percentage is 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.
Solution:
Given, the shopkeeper buys 80 articles of ₹ 2,400
Cost of one article = 2400/80 = ₹ 30
Given, profit percentage = 16%
Now,
Profit percentage = Profit/C.P x 100
16 = Profit/30 x 100
Profit = (16 x 30)/100
= ₹ 4.8
Hence, selling price of one article = C.P + Profit
= ₹ (30 + 4.80)
= ₹ 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.
Solution:
Given,
cost of an article = ₹ 15,500
Repairing cost = ₹ 450
Profit percent = 15%
Now,
Total cost of an article = Cost + Overhead expenses
= ₹15500 + ₹450
= ₹15950
Profit percentage = 15%
Profit percentage = Profit/C.P x 100
15 = Profit/15950 x 100
Profit = (15 x 15950)/100
= 2392.50
Hence, Selling price of the article = C.P + Profit
= ₹(15950 + 2392.50)
= ₹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.
Solution:
Given,
Cost Price (CP) of a VCR = ₹ 8000
The shopkeeper made a loss of 4 % on VCR
So,
This means if Cost Price is ₹ 100, then Selling Price (SP) is ₹ 96.
Now, When Cost Price is ₹ 8000
Selling Price = (96/100 x 8000) = ₹ 7680
Cost Price of a TV = ₹ 8000
Given, the shopkeeper made a profit of 8 % on TV.
This means that if Cost Price is ₹ 100, then Selling Price is ₹ 108.
When Cost Price is ₹ 8000,
Selling Price = (108/100 x 8000) = ₹ 8640
Total Selling Price = ₹ 7680 + ₹ 8640 = ₹ 16320
Total Cost Price = ₹ 8000 + ₹ 8000 = ₹ 16000
Since, total Selling Price total Cost Price ⇒ profit
Profit = ₹ 16320 − ₹ 16000 = ₹ 320
Profit % on the whole transaction = Profit/Total CP x 100
= 320/16000 x 100
= 2%
Hence, the shopkeeper had a gain of 2% on 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?
Solution:
Marked price on jeans = ₹ 1450
Marked price of one shirt = ₹ 850
Total marked price = ₹ (1,450 + 2 × 850)
= ₹ (1,450 +1,700)
= ₹ 3,150
Given, discount percentage = 10%
Discount = ₹ (10/100 x 3150) = ₹ 315
Also, Discount = Marked price − Sale price
₹ 315 = ₹ 3150 − Sale price
So, Sale price = ₹ (3150 − 315)
= ₹ 2835
Hence, the customer will have to pay ₹ 2,835.
7. 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)
Solution:
Selling Price (SP)
Cost Price (CP)
S.P. of one buffalo = ₹ 20,000
The milkman made a gain of 5% while selling one buffalo
So, it means if C.P. is ₹ 100, then S.P. is ₹ 105.
C.P. of one buffalo = 100/105 × 20000
= ₹ 19,047.62
Also, the second buffalo was sold at a loss of 10%
So, it means if C.P. is ₹ 100, then S.P. is ₹ 90
C.P. of other buffalo = 100/90 × 20000
= ₹ 22222.22
Total C.P. = ₹ 19047.62 + ₹ 22222.22 = ₹ 41269.84
Total S.P. = ₹ 20000 + ₹ 20000 = ₹ 40000
Loss = ₹ 41269.84 − ₹ 40000 = ₹ 1269.84
Hence, the overall loss of milkman was ₹ 1,269.84
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.
Solution:
Price of TV = ₹ 13,000
On ₹ 100, the tax to be paid = ₹ 12
Now, on ₹ 13000, the tax to be paid will be = 12/100 × 13000
= ₹ 1560
So, the required amount = Cost + Sales Tax
= ₹ 13000 + ₹ 1560
= ₹ 14560
Hence, Vinod will have to pay ₹ 14,560 for the T.V.
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.
Solution:
Let us assume the marked price be x
Given discount = 20%
Discount percent = Discount/Marked Price x 100
20 = Discount/x × 100
Discount = 20/100 × x
= x/5
Also,
Discount = Marked price – Sale price
x/5 = x – ₹ 1600
x – x/5 = 1600
4x/5 = 1600
x = 1600 x 5/4
= 2000
Hence, the marked price was ₹ 2000.
10. I purchased a hair-dryer for ₹ 5,400 including 8% VAT. Find the price before VAT was added.
Solution:
Price of hair-dryer = ₹ 5,400
VAT percent = 8%
So, 8% VAT means that,
If the price without VAT is ₹ 100,
Then, price including VAT will be ₹ 108
Now,
When price including VAT is ₹ 108,
Then, original price = ₹ 100
When price including VAT is ₹ 5400,
Then, original price = ₹ (100/108 × 5400)
= ₹ 5000
Hence, the price of the hair-dryer before the addition of VAT was ₹ 5,000.
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