Exercise 5.2
1. In the year 2012, it was estimated that there were 36.4 crore Internet users worldw> ide. In the next ten years, that number will be increased by 125%. Estimate the number of Internet users worldw> ide in 2022.
Solution:
Increase in internet users = 125% of 36.4 crore
=
=
=
Estimated number of internet users in 2022 = Number of users in 2012 + Increase in users
=
=
Therefore, the estimated number of internet users worldw> ide in 2022 is 81.9 crore.
2. An owner increases the rent of his house by 5% at the end of each year. If currently its rent is ₹2500 per month, how much will be the rent after 2 years?
Solution:
Rent after 1 year:
Increase = 5% of ₹2500 =
Rent after 1 year = ₹
Rent after 2 years:
Increase = 5% of ₹2625 =
Rent after 2 years = ₹
Therefore, the rent after 2 years will be ₹ 2756.25.
3. On Monday, the value of a company’s shares was ₹7.50. The price increased by 6% on Tuesday, decreased by 1.5% on Wednesday, and decreased by 2% on Thursday. Find the value of each share when trade opened on Fr> iday.
Solution:
Tuesday:
Increase = 6% of ₹7.50 = (6/100) × ₹7.50 = ₹
Value after Tuesday = ₹7.50 + ₹0.45 = ₹
Wednesday:
Decrease = 1.5% of ₹7.95 =
Value after Wednesday = ₹
Thursday:
Decrease = 2% of ₹7.83 =
Value after Thursday = ₹
Therefore, the value of each share when trade opened on Fr> iday was approximately ₹ 7.67.
4. With most of the Xerox machines, you can reduce or enlarge your original by entering a percentage for the copy. Reshma wanted to enlarge a 2 cm by 4 cm drawing. She set the Xerox machine for 150% and copied her drawing. What will be the dimensions of the copy of the drawing be?
Solution:
Original dimensions: 2 cm by 4 cm
Enlargement percentage: 150 %
New dimensions:
Length: 150% of 2 cm =
Width: 150% of 4 cm = (150/100) × 4 cm =
Therefore, the dimensions of the copy of the drawing will be 3 cm by 6 cm.
5. The printed price of a book is ₹150. The discount is 15%. Find the actual amount to be pa> id.
Solution:
Printed price = ₹150
Discount percentage = 15%
Discount amount = 15% of ₹150 =
Actual amount to be paid = Printed price - Discount amount
= ₹
= ₹
Therefore, the actual amount to be paid is ₹127.50.
6. The marked price of a gift item is ₹176 and it is sold for ₹165. Find the discount percent.
Solution:
Marked price = ₹
Selling price = ₹
Discount amount = Marked price - Selling price = ₹ 176 - ₹165 = ₹
Discount percent =
=
=
=
Therefore, the discount percent is 6.25%.
7. A shopkeeper purchased 200 bulbs for ₹10 each. However, 5 bulbs were fused and put into scrap. The remaining were sold at ₹12 each. Find the gain or loss percent.
Solution:
Cost price of 200 bulbs = 200 × ₹10 = ₹
Number of fused bulbs = 5
Number of good bulbs =
Selling price of 195 bulbs = 195 × ₹ 12 = ₹
Since the selling price is greater than the cost price, there is a
Gain = Selling price - Cost price
= ₹
= ₹
Gain percent =
=
=
Therefore, the shopkeeper's gain percent is 17%.
8. Complete the following table with appropriate entries (Wherever possible)
| S. No. | Cost Price (C.P.) | Expenses | Selling Price (S.P.) | Profit | Loss | Profit Percentage | Loss Percentage |
|---|---|---|---|---|---|---|---|
| 1 | ₹750 | ₹50 | ₹80 | ||||
| 2 | ₹4500 | ₹500 | ₹1,000 | ||||
| 3 | ₹46,000 | ₹4000 | ₹60,000 | ||||
| 4 | ₹300 | ₹50 | 12% | ||||
| 5 | ₹330 | ₹20 | 10% |
Solution:
Row 1:
Total Cost = CP + Expenses = ₹
Profit = SP - Total Cost = ₹
SP = CP + Expenses + Profit = ₹
Profit % =
Row 2:
Total Cost = ₹
Profit = ₹
SP = Total Cost + Profit = ₹
Profit % =
Row 3:
Total Cost = ₹
SP = ₹
Profit = ₹
Profit % =
Row 4:
Total Cost = ₹
Profit % =
Profit =
SP = Total Cost + Profit = ₹
Row 5:
Total Cost = ₹
Profit % =
Profit =
SP = Total Cost + Profit = ₹
9. A table was sold for ₹2,142 at a gain of 5%. At what price should it be sold to gain 10%.
Solution:
Selling price with 5% gain = ₹
Let the cost price be 'C'.
Selling price = Cost price + 5% of Cost price
₹ 2142 = C +
₹ 2142 =
C = ₹
C = ₹
Now, to gain 10%:
Selling price with 10% gain = Cost price + 10% of Cost price
New SP = C +
=
= 1.10 × ₹
= ₹
Therefore, the table should be sold for ₹2244 to gain 10%.
10. Gopi sold a watch to Ibrahim at 12% gain and Ibrahim sold it to John at a loss of 5%. If John paid ₹1,330, then find how much did Gopi sell it for?
Solution:
Let the price at which Gopi sold the watch be 'x'.
Ibrahim bought the watch at a 12% gain from Gopi. So, Ibrahim's purchase price = x + 12% of x =
Ibrahim sold the watch to John at a 5% loss. So, John's purchase price = 1.12x - 5% of 1.12x =
We are given that John paid ₹1,330. Therefore:
0.95 × 1.12x = ₹1,330
x = ₹
x = ₹
Therefore, Gopi sold the watch for ₹1250.
11. Madhu and Kavitha purchased a new house for ₹3,20,000. Due to some economic problems, they sold the house for ₹2,80,000.
Find (a) The loss incurred.
Solution:
Purchase price = ₹
Selling price = ₹
Loss incurred = Purchase price - Selling price = ₹ 3,20,000 - ₹2,80,000
= ₹
Therefore, the loss incurred is ₹40,000.
Find (b) The loss percentage.
Solution:
Loss incurred = ₹40,000 (calculated in part (a))
Purchase price = ₹
Loss percentage =
=
= (
=
Therefore, the loss percentage is 12.5%.
12. A pre-owned car show-room owner bought a second-hand car for ₹1,50,000. He spent ₹20,000 on repairs and painting, then sold it for ₹2,00,000. Find whether he gets profit or loss. If so, what percent?
Solution:
Cost price of the car = ₹
Amount spent on repairs and painting = ₹
Total cost price = Cost price + Repair cost
= ₹ 1,50,000 + ₹20,000
= ₹
Selling price of the car = ₹ 2,00,000
Since the selling price is greater than the total cost price, the owner makes a
Profit = Selling price - Total cost price
= ₹2,00,000 - ₹1,70,000
= ₹
Profit percent =
=
=
=
Therefore, the owner gets a profit of ₹30,000, which is approximately 17.65%.
13. Lalitha took a parcel from a hotel to celebrate her birthday with her friends. It was billed with ₹1,450 including 5% VAT. Lalitha asked for some discount; the hotel owner gave an 8% discount on the bill amount. Now find the actual amount that Lalitha has to pay to the hotel owner.
Solution:
Bill amount including 5% VAT = ₹ 1,450
Let the original price of the parcel (before VAT) be 'x'.
x + 5 % of x = ₹ 1,450
x =
x = ₹
The hotel owner gave an 8% discount on the ×bill amount× (which includes VAT).
Discount amount = 8% of ₹1,450
= (
= ₹
Actual amount Lalitha has to pay = Bill amount - Discount amount
= ₹1,450 - ₹116
= ₹
Therefore, Lalitha has to pay ₹1334 to the hotel owner.
14. If GST is included in the price, find the actual price of each of the following.
| S.No | Item | GST% | Bill amount(in ₹) | Original Price(₹) |
|---|---|---|---|---|
| i | Diamond | 3% | ₹ 10,300 | |
| ii | Pressure cooker | 12% | ₹ 3,360 | |
| iii | Face powder | 28% | ₹ 256 |
Solution:
(i) Diamond:
Bill amount (including 3% GST) = ₹
Let the original price be 'x'.
x + (
x = ₹
x = ₹
(ii) Pressure cooker:
Bill amount (including 12% GST) = ₹3,360
Let the original price be 'y'.
y + (
y = ₹
y = ₹
(iii) Face powder:
Bill amount (including 28% GST) = ₹ 256
Let the original price be 'z'.
z + (
z =
z = ₹
15. A Cellphone Company fixed the price of a cellphone as ₹4500. A dealer purchased a cellphone on which he pa> id 12% GST additionally. How much d> id the dealer pay as GST? What is the purchase price of the Cellphone?
Solution:
Price of the cellphone = ₹ 4500
GST percentage = 12 %
GST amount = (
= ₹
Purchase price = Price of cellphone + GST amount
= ₹
= ₹
Therefore, the dealer paid ₹540 as GST. The purchase price of the cellphone is ₹ 5040.
16. A Super-Bazar prices an item in rupees and paise so that when 4% sales tax is added, no rounding is necessary because the result is exactly in ‘n’ rupees, where ‘n’ is a positive integer. Find the smallest value of ‘n’.
Solution:
Let the price of the item in paise be 'x'.
When 4 % sales tax is added, the new price is x + (
For 1.04x to be exactly 'n' rupees (an integer multiple of 100 paise), x must be a multiple of
Then 1.04x = 1.04 × 25k =
We need 26k to be a multiple of 100, or 13k to be a multiple of 50.
Since 13 and 50 are relatively prime, k must be a multiple of 50. The smallest positive integer value for k is
Therefore, x = 25 × 50 =
The price with tax is 1.04 × ₹ 12.50 = ₹
Thus, the smallest value of 'n' is 13.