Embibe Experts Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: Exercise

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 = _____ $\mathrm{m}$

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)

In the picture below two cables supporting an electrical pole from either side of the pole, so that points where cables were fixed on the earth and foot of the pole are in a straight line.

The cable $AC$ and $AB$ are given by equation of straight lines, $12x-5y=0$ and $3x+y 27=0$.  Find the ratio of distances from $AO$ to that of $BO$.

The air traffic controller (ATC) is monitoring the flight path of two flights, flying on the same height. The position coordinates of flight $P$ at two different points of time was $A (23 \mathrm{km} \mathrm{E}, 32 \mathrm{km} \mathrm{N})$ and $B (55 \mathrm{km} \mathrm{E}, 43 \mathrm{km} \mathrm{N})$. The position coordinates of flight $Q$ was $C (26 \mathrm{km} \mathrm{E}, 72 \mathrm{km} \mathrm{N})$ and $D (58 \mathrm{km} \mathrm{E}, 83 \mathrm{km} \mathrm{N})$.

The pilots of the respective flights were told not to deviate from the current straight flight path without confirmation from the ATC, till further notice. Show that the flights will not collide in the event that either or both flights loose contact with the ATC.

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?