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Practice each question, then open the answer or worked solution.
A man got a 10% increase in his salary. If his new salary is ₹1,54,000, find his original salary.
Let the original salary be x
Given that, the new salary is ₹1,54,000
Original salary + Increment = New salary
Given that the increment is 10% of the original salary
So, (x + 10/100 × x) = 154000
x + x/10 = 154000
11x/10 = 154000
x = 154000 × 10/11
= 140000
Therefore, the original salary was ₹1,40,000.
On Sunday, 845 people went to the zoo. On Monday, only 169 people went. What is the per cent decrease in the number of people visiting the zoo on Monday?
Given that on Sunday, 845 people went to the zoo, and on Monday, 169 people went to the zoo.
Decrease in the number of people = 845 – 169 = 676
Thus,
Percentage decrease = (Decrease in the number of people/Number of people who went to the zoo on Sunday) x 100%
= (676/845 x 100)%
= 80%
A shopkeeper buys 80 articles for ₹ 2,400 and sells them for a profit of 16%. Find the selling price of one article.
Given that the shopkeeper buys 80 articles for ₹ 2,400
Cost of one article = 2400/80 = ₹ 30
Profit percentage = 16%
Profit percentage = Profit/C.P. x 100
16 = Profit/30 x 100
Profit = (16 x 30)/100
= ₹ 4.8
Therefore, the selling price of one article = C.P. + Profit
= ₹ (30 + 4.80)
= ₹ 34.80
The cost of an article was ₹ 15,500. ₹ 450 was spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.
The 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
Therefore, the selling price of the article = C.P. + Profit
= ₹(15950 + 2392.50)
= ₹18342.50
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 per cent on the whole transaction.
C.P. of a VCR = ₹ 8000
The shopkeeper made a loss of 4 % on VCR
This means if C.P. is ₹ 100, then S.P. is ₹ 96.
When C.P. is ₹ 8000,
S.P. = (96/100 x 8000) = ₹ 7680
C.P. of a TV = ₹ 8000
The shopkeeper made a profit of 8 % on TV.
This means that if C.P. is ₹ 100, then S.P. is ₹ 108.
When C.P. is ₹ 8000,
S.P. = (108/100 x 8000) = ₹ 8640
Total S.P. = ₹ 7680 + ₹ 8640 = ₹ 16320
Total C.P. = ₹ 8000 + ₹ 8000 = ₹ 16000
Since, total S.P.> total C.P. ⇒ profit
Profit = ₹ 16320 − ₹ 16000 = ₹ 320
Profit % on the whole transaction = Profit/Total CP x 100
= 320/16000 x 100
= 2%
Therefore, the shopkeeper had a gain of 2% on the whole transaction.
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?
Total marked price = ₹ (1,450 + 2 × 850)
= ₹ (1,450 +1,700)
= ₹ 3,150
Given that, the discount percentage = 10%
Discount = ₹ (10/100 x 3150) = ₹ 315
Also, Discount = Marked price − Sale price
₹ 315 = ₹ 3150 − Sale price
∴ Sale price = ₹ (3150 − 315)
= ₹ 2835
Therefore, the customer will have to pay ₹ 2,835.
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 the C.P. of each)
S.P. of each buffalo = ₹ 20,000
The milkman made a gain of 5% while selling one buffalo
This 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%
This 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
Therefore, the overall loss of milkman was ₹ 1,269.84
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.
On ₹ 100, the tax to be paid = ₹ 12
Here, on ₹ 13000, the tax to be paid will be = 12/100 × 13000
= ₹ 1560
Required amount = Cost + Sales Tax
= ₹ 13000 + ₹ 1560
= ₹ 14560
Therefore, Vinod will have to pay ₹ 14,560 for the TV.
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.
Let the marked price be x
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
Therefore, the marked price was ₹ 2000.
I purchased a hair dryer for ₹ 5,400, including 8% VAT. Find the price before VAT was added.
The price includes VAT
So, 8% VAT means that if the price without VAT is ₹ 100,
Then, the price including VAT will be ₹ 108
When price including VAT is ₹ 108, original price = ₹ 100
When price including VAT is ₹ 5400, original price = ₹ (100/108 × 5400)
= ₹ 5000
Therefore, the price of the hair dryer before the addition of VAT was ₹ 5,000.