Applications of Pair of Equations

Q.

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?

1. None of the above

2. $\frac{2}{5}$

3. $\frac{3}{5}$

4. $\frac{1}{4}$

Q.

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay ₹ 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charges and the cost of food per day.

1. ₹ 500, ₹ 50

2. ₹ 300, ₹ 45

3. ₹ 800, ₹ 20

4. ₹ 400, ₹ 30

Q.

State true or false:
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, Yash would have scored 50 marks. Then the total number of questions in the test was 25. (Assuming Yash attempted all questions)

1. True

2. False

Q.

Aruna has only Re1 and Rs.2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then find the number of Re1 and Rs.2 coins Aruna has.

1. 35 and 15
2. 25 and 20
3. 15 and 35
4. 25 and 25

Q.

A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current.

1. 8 km/hr, 3 km/hr

2. 5 km/hr, 3 km/hr

3. 8 km/hr, 5 km/hr

4. 9 km/hr, 6 km/hr

Q.

The units' digit of a two digit number is thrice its tens digit. If 36 is added to the number, the digits interchange their place. Find the number.

1. 26

2. 45

3. 54

4. 62

Q.

Solve the following pair of linear equations by the substitution method:

$$\begin{gathered} 3x-y=3 \\ 9x-3y=9. \end{gathered}$$

Q. A three digit number and is 459 more than sum of its digits. What is the sum of the 2 digit number ab and one digit a?

Q.

State true or false:

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. The number is 18.

1. True

2. False

Q.

A father's age is thrice his son's age. The sum of their ages is 40 years. Find the son's age.

1. 11 years

2. 9 years

3. 10 years

4. 12 years

Q.

Points A and B are 90 km apart from each other on a highway. Car X starts from point A and another car Y starts from point B at the same time. If they travel in the same direction they meet in 9 hours and if they travel in opposite directions they meet in $\frac{9}{7}$ hours. What is the speed of car X?

1. 90 km/hr

2. 40 km/hr

3. 30 km/hr

4. 220 km/hr

Q.

Solve the following:
Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Rs. 100000, how much money did Anima have?

Q.

Solve the following:

If numerator is 2 less than denominator of a rational number and when 1 is substracted from numerator and denominator both, the rational number in its simplest form is $\frac{1}{2}$. What is the rational number?

Q. Question 1 (ii)
Solve the following pair of linear equations by the substitution method.
$s-t=3;\frac{s}{3}+\frac{t}{2}=6$

Q.

A plane left 30 minutes later than the scheduled time. In order to reach the destination 1500 km away in time, it has to increase the speed by 250 km/hr from the usual speed. Find its usual speed.

1. 1000 km/hr

2. 750 km/hr

3. 680 km/hr

4. 800 km/hr

Q.

$A,B,C$ are the three angles of a triangle. If $A-B={15}^{\circ }$, $B-C={30}^{\circ }$, find $\angle$A, $\angle$B and $\angle$C .

Q. The present age of Jacob’s father is three times that of Jacob. After 5 years, the sum of their ages would be 70 years. What's their present ages?

1. 15 years and 45 years
2. 45 years and 25 years
3. 25 years and 35 years
4. 45 years and 12 years

Q.

State true or false:

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. The dimensions of the rectangle are 17 units and 9 units.

1. True

2. False

Q. Question 5
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Q.

One angle of a parallelogram is twice the adjacent angle. What are the angles of the parallelogram?

1. ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$ and ${120}^{\circ }$

2. ${140}^{\circ }$, ${50}^{\circ }$, ${50}^{\circ }$ and ${140}^{\circ }$

3. ${180}^{\circ }$, ${100}^{\circ }$, ${180}^{\circ }$ and ${100}^{\circ }$

4. ${100}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$ and ${80}^{\circ }$

Q. Write four solutions for the following equation.

Q.

Three chairs and two tables cost Rs. 1850. Five chairs and three tables cost Rs. 2850. Then the total cost of one chair and one table is:

1. Rs. 800

2. Rs. 850

3. Rs. 900

4. Rs. 950

Q. Write four solutions for each of the following equations:
(i) $2x+y=7$
(ii) $\pi x+y=9$
(iii) $x=4y$

Q.

Two towns A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. Find the speeds of both the cars.

1. 60 km/h, 40 km/h

2. 55 km/h, 35 km/h

3. 80 km/h, 60 km/h

4. 90 km/h, 50 km/h

Q.

The cost of 5 kg of sugar and 7 kg of rice is ₹153 and the cost of 7 kg of sugar and 5 kg of rice is ₹ 147 find the cost of 6 kg of sugar and 10 kg of rice

Q.

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27 for a book kept for seven days, while Susy paid ₹ 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

1. ₹ 15, ₹ 3

2. ₹ 12, ₹ 4

3. ₹ 20, ₹ 7

4. ₹ 17, ₹ 4

Q.

A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and 48 km downstream in 9 hours. Find the speed of the boat in still water and that of the stream.

1. 6 km/hr, 4 km/hr

2. 10 km/hr, 2 km/hr

3. 14 km/hr, 5 km/hr

4. 44 km/hr, 8 km/hr

Q.

How old will Ravi be after 10 years, if his age was 'x' 10 years ago?

1. x + 20

2. x + 30

3. x + 10

4. x - 20

Q. { One year ago, a man was }7 times as old as his son. The equation of this situation: Take : present age }}{ of father and son }x and }y year respectively)

Q. Question 2
One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II].