Elementary Algebra
- Ramesh and Ganesh had some oranges initially. If Ramesh gave 5 oranges to Ganesh, then Ganesh will have thrice as many oranges as Ramesh. Instead of that, if Ganesh was to give 5 oranges to Ramesh, then they both will have the same number of oranges. Find the ratio of oranges that were distributed between Ramesh and Ganesh ?
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Let the number of oranges Ramesh has be x and the number of oranges Ganesh has be y.
According to the first condition,
y + 5 = 3(x - 5)
⇒ 3x - y + 10 = 0 ...(i)
According to the second condition,
x + 5 = y - 5
⇒ x - y + 10 = 0 ...(ii)Correct Option: A
Let the number of oranges Ramesh has be x and the number of oranges Ganesh has be y.
According to the first condition,
y + 5 = 3(x - 5)
⇒ 3x - y + 10 = 0 ...(i)
According to the second condition,
x + 5 = y - 5
⇒ x - y + 10 = 0 ...(ii)
On subtracting Eq. (ii) from Eq. (i), we get x = 15
On substituting the value of x in Eq.(ii), we get y = 25
∴ The ratio of oranges to be distributed Ramesh and Ganesh = 15:25 = 3:5
- A man covers a distance of 18 km in 5 h party by walking and partly by running. if he walks at 2 km/h and runs at 6km/h, then find the distance he covers by running ?
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Let the distance covered by walking be x km.
Speed while walking = 2 km/h
Time spent on walking = x/2 h
Now, distance covered by runnig = (18 - x) km
Speed while running = 6 km/h
Time spent on running = (18 - x)/6 h
∴x/2 + (18 -x)/6 = 5Correct Option: A
Let the distance covered by walking be x km.
Speed while walking = 2 km/h
Time spent on walking = x/2 h
Now, distance covered by runnig = (18 - x) km
Speed while running = 6 km/h
Time spent on running = (18 - x)/6 h
∴x/2 + (18 -x)/6 = 5
⇒ (3x + 18x - x)/6 = 5
⇒ 2x + 18 = 30
⇒ 2x = 12
⇒ x = 6
∴ The distance covered by running = 18 - 6 = 12 km
- A student was asked to find 2/5th of a number and he instead multiplied it by 5/2. As a result he got an answer which was more than the correct answer by 5208. What was the number ?
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Let the number be x. Then,
5x/2 - 2x/5 = 5208Correct Option: C
Let the number be x. Then,
5x/2 - 2x/5 = 5208
⇒ (25x - 4x)/10 = 5208
⇒ 21x/10 = 5208
⇒ 21x = 5208 x 10
⇒ x = (5208 x 10)/21
⇒ x = 2480
So, the original numbers was 2480.
- If the polynomials ax3 + 4x2 -3x - 4 and x3 - 4x + a leave the same remainder when divided by (x - 3). Then, what is the value of a ?
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Since, p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 -4x + a divided by x - 3, hence p(3) = q(3)
Correct Option: B
Since, p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 -4x + a divided by x - 3, hence p(3) = q(3)
⇒ a x 33 + 4 x 32 + 3 x 3 - 4 = 33 - 4 x 3 + a
∴ a = -1
- Find the remainder when f(x) = x4 - 6x3 + 2x2 + 3x + 1 is divided by (x - 2) ?
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When f(x) = x4 - 6x3 + 2x2 + 3x + 1 is divided by (x - 2), then remainder can be calculated by putting x - 2 = 0
Correct Option: D
When f(x) = x4 - 6x3 + 2x2 + 3x + 1 is divided by (x - 2), then remainder can be calculated by putting x - 2 = 0
i.e. x = 2
Now, put x = 2 in f(x)
f(2) = (2)4 - 6(2)3 + 2(2)2 + 3 x 2 + 1
= 16 - 48 + 8 + 6 + 1 = -17
∴ The remainder will be - 17.
