Applications of Second Degree Equations

Q.

A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/hr$ less, then it would have taken $3$ hours more to cover the same distance. The original speed of the train is ___ km/hr.

1. 40

2. 42

3. 50

4. 45

Q.

Two pipes running together can fill a tank in $11\frac{1}{9}$ minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Q. Question 9
Two water taps together can fill a tank in $9\frac{3}{8}$ hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Q. Two taps running together can fill a tank in 3 $\frac{1}{13}$ hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?

Q.

A chess board contains 64 equal squares and the area of each square is $6.25c{m}^2$. A border around the board is 2 cm wide. Find the length of the side of the chess board.

1. 24 cm

2. 36 cm

3. 32 cm

4. 16 cm

Q.

A man had a certain amount with him. He spent $20\%$ of that to buy an article and $5\%$ of the remaining on the transport. Then he gifted $₹120$. If he is left with $₹1400$, the amount he spent on transport is:

1. $₹380$

2. $₹61$

3. $₹95$

4. $₹80$

Q.

State true or false. A natural number, when increased by 12, equals 160 times its reciprocal. Such a number is 8.

1. True

2. False

Q. A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 kmph. What is the initial speed of the train (in kmph)?

1. 25

Q.

Two pipes running together can fill a cistern in $3\frac{1}{13}$ minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which faster pipe would fill the cistern.

1. 8 minutes

2. 5 minutes

3. 10 minutes

4. 7 minutes

Q.

If Zeba had been younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. Her actual age now is ___ years.

1. $10$

2. $15$

3. $12$

4. $14$

Q.

In a scheme, a pack of three soaps with MRP $₹45$ is available for $₹42$. If it still gives a profit of $5\%$ to the shopkeeper, then find the cost price of the pack?

Q. The length of a rectangular field is three times its breadth. If the area of the field is 147 sq. metres, then what is the length of the field (in metres)?

1. 21

Q.

A natural number has prime factorization given by$\begin{array}{rcl}n& =& 2^x{3}^y{5}^z\end{array}$, where $y$and $z$are such that$\begin{array}{rcl}y+z& =& 5,\frac{1}{y}+\frac{1}{z}=\frac{5}{6}andyz=6\end{array}$. Then the number of odd divisors of$n$, including$1$, is

1. $11$

2. $16$

3. $12$

4. $6$

Q.

Two students, while solving a quadratic equation, committed the following mistakes:
(i) One of them made a mistake in the constant term and got the roots as $5$ and $9$.
(ii) Another one committed an error in the coefficient of $x$ and got the roots as $12$ and $4$.
But, in the meantime, they realised that they are wrong and they managed to get it right jointly.

Find the correct quadratic equation.

1. $x^2-44x+14=0$

2. $2x^2+7x-24=0$

3. $x^2-14x+48=0$

4. $3x^2-17x+52=0$

Q. The diagonal of a rectangular field is 16 m more than the shorter side. If the longer side is 14 m more than the shorter side, then find the lengths of the sides of the field.

Q.

If a train travelled 5 km/hr faster, it would take one hour less to travel 210 km. The speed of the train is:

1. 35 km/hr

2. 60 km/hr

3. 30 km/hr

4. 70 km/hr

Q.

A takes 6 days less than the time taken by B to finish a piece of work. Both A and B together can finish it in 4 days. The time taken by B to finish the work is ___ days.

1. 14

2. 10

3. 8

4. 12

Q. If ​​​​​​$x^2+px+q=0$ and $x^2+qx+p=0$ have a common root, then ____.

1. p + q = 0
2. Both (a) and (b)
3. p = q
4. p + q = -1

Q.

A turtle lives in a garden and a hedgehog lives in the woods. They leave their homes at the same time walk toward each other and meet in $5hours$ . The turtle walks $10metersperhour$ slower than the hedgehog. If the turtle had left home $4\frac{1}{2}hours$ earlier than the hedgehog had left his home, the two would meet $150m$ from the woods. Find the distance between the garden and the woods.

Q.

The product of two consecutive positive odd numbers is 63. Select the correct options.

1. One of the numbers is 5

2. One of the numbers is 3

3. One of the numbers is 7

4. One of the numbers is 9

Q.

The sum of the squares of two consecutive natural numbers is 421. The numbers are

1. 12 and 13

2. 13 and 14

3. 14 and 15

4. 15 and 16

Q.

The sum of two numbers is 15. The sum of their reciprocals is $\frac{5}{18}$. Find the numbers.

1. 7 and 8

2. 9 and 6

3. 10 and 5

4. 11 and 4

Q.

The product of two consecutive positive even number is 48. Select the correct numbers.

1. 7

2. 6

3. 9

4. 8

Q.

$Twopipesrunningtogethercanfillacisternin2\frac{8}{11}minutes.Ifonepipetakesoneminutemorethantheothertofillthecistern,findthesumofindividualtimeinwhicheachpipewillfillthecistern.$

1. 5 min

2. 11 min

3. 10 min

4. 6 min

Q. The sum of two natural numbers is 8. Determine the numbers, if the sum of their reciprocals is $\frac{8}{15}$.

Q.

A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/hr$ less, then it would have taken $3$ hours more to cover the same distance. The speed of the train is ___ kmph.

1. 48

2. 40

3. 45

4. 35

Q. Three consecutive positive integers are taken such that sum of the square of the first number and the product of other two numbers is 232. Find the integers.

1. 12, 13, 14
2. 11, 12, 13
3. 5, 6, 7
4. 10, 11, 12

Q.

How many consecutive natural numbers starting from 1 can be added to get 5050?

1. 101

2. 98

3. 99

4. 100

Q.

300 chocolates are distributed equally among a certain number of students. Had there been 10 more students, each would have received one chocolate less. The number of students is ___ .

1. 45

2. 55

3. 48

4. 50

Q.

If in a right triangle, the hypotenuse is 20 m and the difference between the lengths of other sides is 4 m. Then, the sides are 14 and 18.

1. False

2. True