Q 01. Jacob spends 8% of his income on transport and 60% of the remaining amount on food. After these expenses, he managed to save $662.4. His income is: Ops: A. $900 B. $1100 C. $1800 D. $1000 Q 02. If the cost price of an item is $840, the mark up is 15% and the discount is 10%, then find the profit percent. Ops: A. 4.8% B. 6.2% C. 7% D. 3.5% Q 03. The ratio of water and oil in a mixture of 72 litres is 11 : 13 . How many litres of water must be added to the mixture to make the ratio 5 : 4? Ops: A. 22.75 litres B. 15.75 litres C. 19.56 litres D. 14.89 litres Q 04. Incomes of Sophia and Alice are in the ratio of 7 : 9 and each of them saves $360. Find Sophia's income, if the ratio of their expenditures is 2 : 3? Ops: A. $1420 B. $1080 C. $840 D. $1360 Q 05. Rachel bought a bag for $750 and sold it for a loss of $32. What is the selling price of the bag? Ops: A. $825 B. $782 C. $850 D. $718

Sure, let's solve these problems one by one.

Q 01. Jacob spends 8% of his income on transport and 60% of the remaining amount on food. After these expenses, he managed to save $662.4. His income is:

Let's assume Jacob's income is X.

First, he spends 8% on transport, so he has 92% of his income left, which is 0.92X.

Then he spends 60% of the remaining amount on food, so he has 40% of his remaining income left, which is 0.4 * 0.92X = 0.368X.

We know that this amount is $662.4, so we can set up the equation 0.368X = 662.4.

Solving for X gives us X = 662.4 / 0.368 = $1800.

So, the answer is C. $1800.

Q 02. If the cost price of an item is $840, the mark up is 15% and the discount is 10%, then find the profit percent.

The marked price will be 115% of the cost price, which is 1.15 * 840 = $966.

The selling price after a 10% discount will be 90% of the marked price, which is 0.9 * 966 = $869.4.

The profit is the selling price minus the cost price, which is 869.4 - 840 = $29.4.

The profit percent is the profit divided by the cost price, times 100%, which is (29.4 / 840) * 100% = 3.5%.

So, the answer is D. 3.5%.

Q 03. The ratio of water and oil in a mixture of 72 litres is 11 : 13 . How many litres of water must be added to the mixture to make the ratio 5 : 4?

The total amount of water in the mixture is (11 / 24) * 72 = 33 litres.

Let's say we need to add X litres of water to make the ratio 5 : 4. The total amount of water will then be 33 + X, and the total amount of the mixture will be 72 + X.

We can set up the equation (33 + X) / (72 + X) = 5 / 4.

Solving for X gives us X = 15.75 litres.

So, the answer is B. 15.75 litres.

Q 04. Incomes of Sophia and Alice are in the ratio of 7 : 9 and each of them saves $360. Find Sophia's income, if the ratio of their expenditures is 2 : 3?

Let's say Sophia's income is 7X and Alice's income is 9X. Their savings are equal, so their expenditures are also in the ratio of 7 : 9, which is 7X - 360 = 2 and 9X - 360 = 3.

We can set up the equation 7X - 2 = 9X - 3.

Solving for X gives us X = 180.

So, Sophia's income is 7 * 180 = $1260.

So, the answer is not in the options.

Q 05. Rachel bought a bag for $750 and sold it for a loss of$32. What is the selling price of the bag?

The selling price is the cost price minus the loss, which is 750 - 32 = $718.

So, the answer is D. $718.