Question: Two candles of the same height are lighted at the same time. The first candle is consumed in 4 hours and the second one in 3 hours. Assume that each candle burns at the same rate. In how many hours will the first candle measure twice the height of the second candle?
(A) 1 hour and 12 minutes
(B) 2 hours and 24 minutes
(C) 3 hours and 45 minutes
(D) 4 hours and 10 minutes
(E) 4 hours and 48 minutes
Correct Answer: B
Solution and Explanation:
Approach Solution 1:
After any given time(t), length of first candle= Lt/4
After any given time(t), length of second candle= L−Lt/3
Time(t) after the first candle measure twice the height of the second candle
L−Lt/4= 2*[L−Lt/3]
1−t/4= 2−2t/3
2t/3−t/4= 1
8t−3t/12= 1
5t=12
t=2.4 hours= 2 hours and 24 minutes
Approach Solution 2:
For candle A time taken for 100% bearing= 4 hour
So in 1 hour it burns for 25% (100/4)
So, after 1 hr. 25/100 i.e., 1/4 of it has burn 1
Hence, after x hours, amount burnt= x/4
So, amount left= 1−x/4=4−x/4
Simply for candle B, let no assume that its height is half of candle A after x hours.
So, after x hours, part vemacing= 1-x/3= 3-x/3
According to question,
4-x/4= 1(3-x/3)
i.e, Height of candle A=2×. Height of candle B.
Therefore, 12-3x= 24-8x
=> 5x= 12
x= 12/5
= 2.5
So, after 2.4 hours, the height of candle 4 is twice that of candle B.
Approach Solution 3:
Let, h0=initial height of both candles, t=initial time of burning of both candles, h1=current height of first candle, h2=current height of second candle
=> h1=h0-(h0*t)/4; h2=h0-(h0*t)/3. Putting these eqs in h1=2*h2
=> 1-t/4 = 2(1-t/3)
=> t=12/5 h = 2.4 h = 2h and 24min
“Two candles of the same height are lighted at the same time.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
Suggested GMAT Problem Solving Samples
- The Owner of A Local Jewellery Store Hired 3 Watchmen to Guard his Diamonds GMAT Problem Solving
- What is the smallest integer n for which 25^n>5^12 GMAT Problem Solving
- Ten Coins are Tossed Simultaneously. In how many of the Outcomes GMAT Problem Solving
- A Pool can be Filled in 4 Hours and Drained in 5 Hours GMAT Problem Solving
- If x^2 − 2 < 0, which of the following specifies all the possible GMAT Problem Solving
- A Train Approaches A Tunnel AB. Inside The Tunnel Is A Cat Located GMAT Problem Solving
- A Dairyman Pays Rs. 6.40 Per Liter Of Milk GMAT Problem Solving
- John is 20 years older than Brian. 12 years ago, John was twice as old GMAT Problem Solving
- A Train Overtakes Two Persons Who Are Walking In The Same Direction GMAT Problem Solving
- If 1/x − 1/x+1= 1/x+4, Then x could be GMAT Problem Solving
- If x = - |x|, Then Which One of the Following Statements GMAT Problem Solving
- A Bag Contains 4 Red and 3 Black Balls. A Second Bag Contains 2 Red GMAT Problem Solving
- A Mixture of 40 Litres of Milk and Water, Contains 20% of Water GMAT Problem Solving
- A Candidate is Required to Answer 6 Out of 10 Questions Divided into 2 Groups GMAT Problem Solving
- Company XYZ had $498.2 Million in Profits for the Year GMAT Problem Solving
- If -2 < a < 11 and 3 < b < 12, Then Which of the Following is NOT Always True GMAT Problem Solving
- Karan and Arjun run a 100-metre Race, Where Karan Beats Arjun by 10 metres GMAT Problem Solving
- Set T consists of all points (x, y) such that \(x^2+y^2=1\) GMAT Problem Solving
- How Many Natural Numbers Not Exceeding 4321 can be Formed GMAT Problem Solving
- The Figure below Shows an Equilateral Triangle ABC Tangent GMAT Problem Solving
- In an Isosceles Triangle PQR, If ∠Q = 80 Degrees, Then What is The GMAT Problem Solving
- If x=10^{10},\frac{x^2+2x+7}{3x^2-10x+200} is closest to GMAT Problem Solving
- If set S Consists of all Different Solutions of Equation |x – 4| = x, What is the Range of Set S GMAT Problem Solving
- Two Members of a Club are to be Selected to Represent the Club GMAT Problem Solving
- The Square Root of 24336 is Exactly GMAT Problem Solving
- A Certain Purse Contains 30 Coins, Each Coin is either a Nickel or GMAT Problem Solving
- Which of the Following is Equal to the Value of 2^5+2^5+3^5+3^5+3^5 ? GMAT Problem Solving
- The Price of a Certain Painting Increased By 20% During the First Year GMAT Problem Solving
- The Population of the Village is 5500. If the Number of Males Increase GMAT Problem Solving
- Two Vessels A and B Contain Milk and Water Mixed in the Ratio 8:5 GMAT Problem Solving
- A Dealer Offers a Cash Discount of 20%. Further, a Customer Bargains GMAT Problem Solving
- There are Two Vessels A and B. Vessel A is Containing 40 Litres of GMAT Problem Solving
- At A Certain Fruit Stand, The Price Of Each Apple Is 40 Cents GMAT Problem Solving
- The Coordinates Of Vertices P And Q Of An Equilateral Triangle PQR Are GMAT Problem Solving
- A Certain Roller Coaster has 3 Cars, and A Passenger is Equally Likely GMAT Problem Solving
- A Manufacturer Produces a Certain Men's Athletic Shoe in GMAT Problem Solving
- In The Figure Shown Below, The Area of Square Region ACEG is 729 GMAT Problem Solving
- How Many Dimes are There in 4x - 1 Cents? (1 dime = 10 cents) GMAT Problem Solving
- In How Many Ways The Letter Of The Word "Family" Can Be When GMAT Problem Solving
- A Fair Coin Is Tossed 4 Times. What Is The Probability Of Getting At GMAT Problem Solving
- In A Sequence 1, 2, 4, 8, 16, 32, ... Each Term After The First Is Twice GMAT Problem Solving
- What Is The Sum Of Odd Integers From 35 To 85, Inclusive? GMAT Problem Solving
- If 2p + 1/p = 4, Then what is the Value of p^3 + 1/8p^3 ? GMAT Problem Solving
- There are 12 Pipes that are Connected to a Tank. Some of them are fill GMAT Problem Solving
- A wire is cut into three equal parts. The resulting segments are then cut GMAT Problem Solving
- If x = -3, What Is The Value Of -3x^2? GMAT Problem Solving
- There Were R Red Balls And Y Yellow Balls In A Bag. Three Red Balls GMAT Problem Solving
- With An Average Speed Of 40 Km/H, A Train Reaches Its Destination On GMAT Problem Solving
- A Photographer Will Arrange 6 People Of 6 Different Heights GMAT Problem Solving
- What Is The Radius Of The Incircle Of The Triangle Whose Sides Measure GMAT Problem Solving
Comments