Ramya, playing a game of treasure hunt through a maze whose sketch is given below. She knows that a straight line connects location $A$ with the treasure location $D$, and worked out line equation connecting these two locations. Then based on her current coordinates she worked out equations of straight line, to check if her current path is aligned with the planned path.

The equations were $3x-2y+1=0$, $4x-\left(\frac{8}{3}\right)y+\left(\frac{4}{3}\right) = 0$. Ramya got confused looking two different equations and thought she lost her way. Is it true? 

A student generated a sketch of a triangular structure as in the figure below. The line equation for the slant edges of the structure was used to get a high definition sketch. The equations are $3a-8h+10=0$ and $3a+2h-40=0$. Find the height of the structure as per the sketch.

The height of the structure as per the sketch = _____ $\mathrm{m}$

A plumber has fixed fee which he charges once he is hired for the service. He also charges an hourly fee for his work. For $3$ hours work, he charged $₹ 1,150$ and for $5$ hours work he charged $₹ 1,750$.

The hourly rate charged by the plumber is $₹$ _____.

A person travels $300 \mathrm{km}$ by train and by car. He spent $4 \mathrm{hours}$ to travel $60 \mathrm{km}$ by train and the rest by car. Another time, he took $10$ minutes longer when he travelled $100 \mathrm{km}$ by train and the remaining by car.

Find the speed of the train, assuming that the average speed of train and car is the same on both occasions.

The speed of the train is _____ $\mathrm{km}/\mathrm{hr}$.

Drivers are fined $₹500$ for exceeding the speed limit by up to $15 \mathrm{km}/\mathrm{h}$, and $₹1,000$ for exceeding the speed limit by more than $15 \mathrm{km}/\mathrm{h}$. In one night, a policeman gave out $25$ speeding fines worth a total of$₹16,000$

_____ drivers were caught exceeding the speed limit by more than $15 \mathrm{km}/\mathrm{h}$.

A local administration contracted an NGO to give packed fruits for children on the occasion of a festival, where each pack contains $3$ oranges and $2$ apples. The NGO bought two batches of fruits, where the first batch costing $₹2212$, had $50$ oranges, and $62$ apples.  The second batch costing $₹1892$, had $45$ oranges and $52$ apples. The cost of packaging each fruit packet is $12.5\%$ of the cost of fruits in the packet. 

Amount of$₹$_____  should the NGO charge the local administration for each packet of fruits in order to make the entire transaction without profit or loss.

A mason is building a wall of $90 \mathrm{ft}$ long using $12 \mathrm{inch}$ and $9 \mathrm{inch}$ bricks. He had to use 108 bricks in all to make first single lane of bricks for the wall.

He used _____ bricks that are of $12 \mathrm{inch}$.

$2$ men and $3$ women can together finish an embroidery work in $13$ days, while $3$ men and $2$ women can finish it in $12$ days. Then the time taken by $2$ women and $2$ man to complete the same work is _____ days. (Give the answer correct upto one decimal place)

A stick $40 \mathrm{cm}$ long, was snapped into two pieces as shown below. One piece is $10 \mathrm{cm}$ longer than the other.

The length of the longer piece is _____ $\mathrm{cm}$.