The marked price of a toy is same as the percentage of GST that is charged. The price of the toy is ₹ 24 including GST. Taking the marked price as x, form an equation and solve it to find x.

Case Study I

Some students planned a picnic. The total budget for hiring a bus was ₹ 1440. Later on, eight of them refused to go and instead paid their total share of money towards the fee of one economically weaker student of their class and thus, the cost for each member who went for picnic is increased by ₹ 30.

1. If x students planned for the picnic, then the share for hiring the bus per student who went for the picnic, was :

1. ₹ 30x

2. ₹ 1440x

3. ₹ $\dfrac{1440}{x}$

4. ₹ $\dfrac{1440}{x - 8}$

2. The algebraic representation of the given information in the form of a quadratic equation is:

1. x² − 8x − 384 = 0

2. x² + 8x − 384 = 0

3. x² − 8x − 184 = 0

4. x² + 8x − 184 = 0

3. How many students went for the picnic?

1. 24

2. 16

3. 32

4. 2

4. How much money was paid towards the fee?

1. ₹ 280

2. ₹ 340

3. ₹ 420

4. ₹ 480

5. What would be the share of each student if all the students had attended the picnic?

1. ₹ 90

2. ₹ 30

3. ₹ 60

4. none of these

Case Study III

Two water taps together fill a tank in 1 $\dfrac{7}{8}$ hours. The tap with larger diameter takes 2 hours less than the tap with smaller one to fill the tank completely. Based on the above information, answer the following questions:

1. If time taken by the tap with smaller diameter to fill the tank alone be x hours, then part of the tank filled by the tap with larger diameter alone in 2 hours is:

1. 2(x + 2)

2. 2(x - 2)

3. $\dfrac{2}{x + 2}$

4. $\dfrac{2}{x - 2}$

2. The quadratic equation representing the given information is:

1. 4x² − 23x + 15 = 0
2. 2x² − 23x + 15 = 0
3. 4x² + 23x − 15 = 0
4. 2x² + 23x − 15 = 0

3. Time taken by the larger tap to fill the tank alone is:

1. 5 hours
2. 3 hours
3. 7 hours
4. none of these

4. The part of the tank which can be filled by the smaller tap in 3 hours is:

1. $\dfrac{1}{3}$

2. $\dfrac{1}{5}$

3. $\dfrac{3}{5}$

4. $\dfrac{3}{7}$

5. The part of the tank which can be filled by the larger tap in $1\dfrac{1}{4}$ hours is:

1. $\dfrac{5}{12}$

2. $\dfrac{3}{5}$

3. $\dfrac{5}{8}$

4. $\dfrac{3}{8}$

Case Study IV

A motorboat whose speed in still water is 24km/hr, takes 1 hour more to go 32 km upstream than to return downstream to the same spot . Based on this information answer the following questions

1. What is the speed of the motorboat in going upstream, if speed of the stream is x km/hr?

1. (x − 24) km/hr
2. (24 − x) km/hr
3. (x + 24) km/hr
4. none of these

2. The quadratic equation which represents the given information is:

1. x² − 64x − 576 = 0
2. x² + 64x + 576 = 0
3. x² + 64x − 576 = 0
4. x² − 64x + 576 = 0

3. Speed of the motorboat in going downstream is:

1. 16 km/hr
2. 8 km/hr
3. 28 km/hr
4. 32 km/hr

4. Time taken by the motorboat to go 272 km downstream is:

1. $8\dfrac{1}{2}$ hours

2. 17 hours

3. $12\dfrac{1}{2}$ hours

4. $6\dfrac{1}{2}$ hours

5. Time taken by the motorboat to go 80 km upstream and then to return back to the same spot is:

1. $5\dfrac{1}{2}$ hours

2. $6\dfrac{1}{2}$ hours

3. $7\dfrac{1}{2}$ hours

4. $8\dfrac{1}{2}$ hours