Linear Equations in Two Variables Quiz

Find the value of a and b from the given expression: 11/(a + b) + 2(a -b) = 11 22/(a + b) + 3(a - b) = 17

1. a = 10, b = 6
2. a = 8, b = 6
3. a = 6, b = 3
4. a = 8, b = 3

Answer: (d) a = 8, b = 3

In the given question below, there are two statements marked as Assertion (A) and Reason (R). Mark your answer as per the codes provided below. Assertion: The graph of the linear equation x - 2y = 1 passes through the point (3, 1). Reason: Any point lying on the graph of the equation is not a solution of x - 2y = 1.

1. Both A and R are true and R is the correct explanation of A.
2. Both A and R are true but R is not the correct explanation of A.
3. A is true but R is false.
4. A is false but R is true.

Answer: (c) A is true but R is false.

The second angle of a triangle is three times as large as the first. The measure of the third angle is 40o greater than that of the first angle. What is the value of the largest angle?

1. 84o
2. 90o
3. 78o
4. 68o

Answer: (a) 84o

It takes only half the pool to be filled. How long would it take 12 hours to fill a swimming pool using two pipes? If the larger pipe is used for 4 hours and the smaller pipe for 9 hours, how much time larger pipe alone take to fill the pool?

1. 15 hours
2. 30 hours
3. 20 hours
4. 10 hours

Answer: (c) 20 hours

An overseas phone call is charged at one rate (a fixed amount) for the first minute and at a different rate for each additional minute. If a 7-minute call costs $10 and a 4-minute call costs $6.40. Find the rate for each additional minute is $1.2 rate.

1. $2, $1
2. $2.80, $1.20
3. $3.80, $1.20
4. $2.80, $2.20

Answer: (b) $2.80, $1.20

Donna is late for a sales meeting after travelling from one town to another at a speed of 32 mph. If she had travelled 4 mph faster, she could have made the trip in 1 hour less time. How far apart are the towns?

1. 288 miles
2. 200 miles
3. 150 miles
4. 156 miles

Answer: (a) 288 miles

Points C and D are 120 km apart from each other on a straight road. A car starts from C with speed m km/h and another from D with speed n km/h at the same time. If they travel in the same direction and meet after 8 hours, the sum of the speed of C's and D's is 60 km/h.What is the value of D's speed?

1. 22 km/h
2. 22.5 km/h
3. 37.5 km/h
4. 10 km/h

Answer: (b) 22.5 km/h

A boat covers a round trip journey between two points A and B in a river in T hours. If its speed in still water becomes 2 times, it would take 80T/161 hours for the same journey. Find the ratio of its speed in still water to the speed of the river.

1. 11: 1
2. 1 : 11
3. 3 : 11
4. 4 : 11

Answer: (a) 11: 1

Read the passage and answer the following question: A public storage facility rents two types of storage lockers: small and large. Each small storage locker provides 200 square feet of storage space, while each large storage locker offers 800 square feet of space. The facility has a total of 54 storage lockers, which together provide 22,800 square feet of storage space. How many large storage lockers does the facility have based on these two conditions?

1. 11
2. 20
3. 19
4. 15

Answer: (b) 20

Read the passage and answer the following question: A public storage facility rents two types of storage lockers: small and large. Each small storage locker provides 200 square feet of storage space, while each large storage locker offers 800 square feet of space. The facility has a total of 54 storage lockers, which together provide 22,800 square feet of storage space. If the facility charges $50 per month for renting a small locker and $120 per month for renting a large locker. If the facility earns $4,200 in rental income per month, how many large lockers are being rented?

1. 11
2. 15
3. 18
4. 21

Answer: (d) 21