Question: The temperature of Delhi and Lucknow were in the ratio 3:5 in July and 2: 3 in August. The percentage increase in temperature from August to September is twice as from July to August for Delhi and same as for July to August for Lucknow. If the ratio of the sum of the temperatures of these two cities in August and July was 5: 4, then answer the following questions.
Q1. What was the percentage increase in temperature of Lucknow from July to August?
Q2. What was the value of the ratio (Temperature of Lucknow in September/Temperature of Delhi in September)?
Q3. If temperature of Delhi in August was 20°C then what was the sum of the temperatures of these two cities in September?
“The temperature of Delhi and Lucknow were in the ratio 3:5 in July”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
Asked: If the ratio of the sum of the temperatures of these two cities in August and July was 5: 4, then answer the following questions.
July:-
Temperature of Delhi = 3x
Temperature of Lucknow = 5x
August: -
Temperature of Delhi = 2y
Temperature of Lucknow = 3y
The percentage increase in temperature from August to September is twice as from July to August for Delhi
(2y/3x - 1) = 2(z/2y -1)
(2y-3x)/3x = 2(z-2y)/2y = (z-2y)/y
y(2y-3x)/3x = (z-2y)
z = 2y + y(2y-3x)/3x
The percentage increase in temperature from August to September is the same as for July to August for Lucknow.
(3y/5x-1) = (z/3y-1)
z = 9yˆ2/5x
September: -
Temperature of Delhi = 2y + y(2y-3x)
Temperature of Lucknow = 9yˆ2/5x
The ratio of the sum of the temperatures of these two cities in August and July was 5: 4
(2y+3y)/(3x+5x) = 5y/8x = 5/4
y = 2x
August: -
Temperature of Delhi = 2y = 4x
Temperature of Lucknow = 3y = 6x
September: -
Temperature of Delhi = 2y + y(2y-3x)/3x = 4x + 2x(4x-3x)/3x = 4x + 2x/3 = 14x/3
Temperature of Lucknow = 9yˆ2/5x = 9*4xˆ2/5x = 36x/5
Q1. What was the percentage increase in temperature of Lucknow from July to August?
6x/5x - 1 = 1/5 = 20%
Q2. What was the value of the ratio (Temperature of Lucknow in September/Temperature of Delhi in September)?
(36x/5)/(14x/3) = 36*3/5*14 = 54/35
Q3. If temperature of Delhi in August was 20°C then what was the sum of the temperatures of these two cities in September?
Temperature of Delhi in August = 2y = 4x= 20
y = 10; x = 5
Sum of temperatures of Delhi & Lucknow in September = 14x/3 + 36x/5 = 14*5/3 + 36*5/5 = 70/3 + 36 = 23 1/3 + 36 = 59 ⅓
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