Mpho's bank account is overdrawn by M485.
(a) She deposits M230 into the account. How much does she now owe the bank?

(b) What further deposit should she make to give her account a balance of M150?

In 2014, a street vendor made a profit of M2160. This was 8% more than the profit made in 2013.
Find the profit made in 2013.

(a) Mpho's salary is M4 400.
(i) Calculate her new salary after a 5% increase.

(ii) The M4 400 was a 10% increase on her previous salary. Calculate Mpho's previous salary.

(b) Thato and Pule share M3 500 in the ratio 3 : 2. Calculate Pule's share.

A trader sold an item to a shopkeeper making 20% profit. The shopkeeper later sold it for M1 560 making a 30% profit.
Calculate the price which the trader paid for the item.

A 4-year investment at 15% compound interest per year yields a total savings of M15,900.
The principal amount for the investment can be expressed in the form $M1.59\times \frac{{\left({10}^x\right)}^y}{A^y}$.
Find the values of A, x and y.

(a) Maema earns M4500 of which he spends 20% on food.
(i) Calculate the amount of money spent on food.

(ii) Leru spends 18% of his salary on food.
This amount is 36% more than the amount Maema spends on food.
Calculate Leru's salary.

(iii) Express as a ratio in its simplest form, the amount Leru spends on food to the amount Maema spends on food.

(b) Pule buys enough potatoes and cabbage for 35 needy people.
(i) On average 10 potatoes weigh 2.4 kg.
Each needy person is to get 7 potatoes.
Calculate the total mass of potatoes that Pule buys.

(ii) Pule buys 110 kg lot of cabbages but loses y% due to transportation on the lot.
Write an expression in terms of y, for the mass of cabbage each person gets.

(c) White bank offers a 5.5% simple interest per year.
Yellow bank offers r% compound interest per year.
Find r if the banks yield equal interest in 3 years.

Tau sells a car at M32 500 making a loss of 20%.
(a) Calculate the price Tau paid for the car.

(b) Tau invests the M32 500 in a bank that offers:
• compound interest for the first 4 years at 3% per annum, then
• simple interest for the next 6 years at 5% per annum.
Calculate the total interest obtained.

(a) The cash price of a mobile set is 10% less than the hire purchase price.
A customer buys a mobile set on a hire purchase and pays a deposit of M300 followed by 12 monthly instalments of M150.
Calculate:
(i) The cash price,

(ii) The rate of interest charged on the cash price to determine the hire purchase price.

(b) A bus travelling at an average speed of 60 km/h left a bus stop at 8.15 am.
A taxi left the bus stop at 9.00 am and overtook the bus at 10.45 am.
(i) How much time, in hours, did the bus take before it was overtaken.

(ii) Find the average speed of the taxi.

A farmer has 540 bags of wet sorghum each having a mass of 96 kg.
After the sorghum was left to dry, it is found that mass of dried sorghum : mass of wet sorghum = 15 : 16.
(a) Calculate the total mass lost during drying.

(b) A trader bought the 540 bags of dried sorghum at M168.75 per bag.
He then repacked them into 75 kg bags.
He transported them to a market in loads of up to 162 bags per trip.
(i) Find the minimum number of trips required to transport all the sorghum.

(ii) The trader paid M250 per trip and sold all the bags of dried sorghum to make a profit of 26%.
Calculate the selling price of each bag.

The table shows the number of coffee tins of sizes 125 g, 250 g and 500 g delivered to shops A, B and C.

	Coffee packets
	125 g	250 g	500 g
Shop A	50	100	300
Shop B	60	150	40
Shop C	80	200	70

(a) Find:
(i) The total number of coffee tins delivered to shop B.

(ii) The total mass in kg, of coffee tins delivered to shop C.

(b) The cost prices of 125 g, 250 g and 500 g are M16, M34 and M60 respectively.
Write a column matrix to represent the prices of the tins.

(c) Find the matrix that represents the total cost of the tins to each shop.

(a) A car costs M120 000.
Limpho buys the car on hire purchase.
He pays 40% deposit and M1 365 monthly for 60 months.
(i) Find the amount of deposit paid.

(ii) Find the extra cost of buying the car on hire purchase.

(iii) Calculate the percentage rate per year of simple interest Limpho is charged on hire purchase for the car.

(b) M56 000 is invested at a rate of 3.2% compound interest each quarter.
(i) Find, in its simplest form, an expression in terms of n, for the value of the investment after n years.

(ii) Find the interest earned after 3 years.

(a) Manka sells his car for M39 995 and makes a loss of 5% on the cost price of the car.
Calculate the cost price.

(b) The value of a house depreciates from M50 000 by 4% every year.
Calculate the value of the house after three years.

(c) Palesa invests M6 400 at the rate of 12.5% compound interest per year.
Calculate the number of years in which her investment will be worth a total amount of M9 112.50.

(a) Neo buys a roof-bike which has a price of M7 200.
He pays 60% of this price and then pays M800 per month for 6 months.
(i) How much does Neo pay altogether?

(ii) How much more or less than the original price does Neo pay for this bike?

(iii) Express your answer in part (a)(ii) as a percentage of M7 200.

(b) Tau pays M8075 for a giant-bike in a sale.
The original price has been reduced by 15%.
Calculate the original price of the giant-bike.

(c) Two brothers, Mpho and Lefa, invest money at two different Banks, A and B.
Mpho invests M3000 at Bank A at 5% simple interest per year.
Lefa invests M3000 at Bank B at 4.9% compound interest per year.
(i) How much will Mpho have at the end of 4 years?

(ii) Who will have more money after 4 years? Support your answer with working.

(iii) How much more will one brother have than the other?

Pule and Thabo receive a sum of money from their father and share it in the ratio 3 : 2.
Thabo receives M1430.40.
(i) Calculate the total amount they received from their father.

(ii) Their father invests M6000 in company A and M5000 in company B.
Company A pays simple interest at rate of 4% per year.
Company B pays compound interest at the rate of 5% per year.
From which company will he get more interest after 5 years and by how much?

(a) The price of a car was M96 000.
The price increased by 30% and later decreased by 20%.
Calculate the overall percentage increase in the price of the car.

(b) A sum of M8 000 was invested for 4 years at 6.4% interest compounded annually.
Calculate the value of the investment after 4 years.

(a) Pork is sold at M50.35 per kilogram on a Tuesday.
(i) Sello buys 7 kilograms of pork on a Tuesday and pays M400.00.
Calculate the amount of change he received after paying.

(ii) The M50.35 price was an increase of 6.5% of the Monday price.
Calculate the price per kg of pork on Monday.

(b) Pork weighing 350 kg, correct to the nearest 10 kg, is brought for slicing.
Slices are packed into portions of 5.25 kg, correct to the nearest 10 grams.
Calculate the largest possible number of portions that could be packed.

(c) Mohoke changed £15.00 to M315.50 to buy a T-shirt on Wednesday.
On Thursday the exchange rate changed to M1 = £0.04733.
If he bought the T-shirt on Thursday, would he pay more or less, and by how much?
Give your answer in Maloti.

(a) A clearance sale at a clothing shop lasts for four days only.
The sale starts on Thursday and ends on Sunday.
For each day of the sale, prices are reduced by 10% of the price on the previous day.
(i) On Wednesday before the start of the sale, a dress was M199.
Thato bought it on Friday.
How much did Thato pay for the dress?

(ii) Lineo bought the same dress as that of Thato on Sunday.
How much less did Lineo pay than Thato?

(iii) On Thursday, Neo paid M360 for his pair of trousers.
What was the price on Wednesday?

(iv) How many days would it take for the original prices to be reduced by more than 25%?

(b) There are two companies from which Neo can borrow money.
Company A: charges 1% compound interest per month.
Company B: charges 12% simple interest per annum.
Neo borrows M800.00 for two years.
Calculate the difference in interest Neo would have to pay if he borrows money in either of the two companies.

Mr Tau invests M10 000 at r% simple interest per year.
He receives a total of M11 500 at the end of 3 years.
(a) Calculate the value of r.

(b) Mr Tau then uses 20% of the M11 500 to pay school fees.
Calculate the amount paid for the school fees.

(c) He also shares M5 000 among daughters Lineo and Mapule in the ratio 2 : 3.
(i) Calculate the amount Lineo receives.

(ii) Mapule takes M1 000 from her share and invests it at 10% compound interest per year.
After how many years will her investment be worth M1331?

(d) Mapule sells a watch for M180 making a profit of 20%.
Calculate the price Mapule paid for the watch.

(e) Lineo bought a watch costing M240.
She later sold it for M196.
Calculate her percentage loss.