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Rev99
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The temperature of Delhi and Lucknow were in the ratio 3:5 in July... Updated on: 22 Jul 2022, 07:48
Originally posted by Rev99 on 22 Jul 2022, 01:19.
Last edited by Rev99 on 22 Jul 2022, 07:48, edited 1 time in total.
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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?

EDIT: This is a CAT related question.
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The temperature of Delhi and Lucknow were in the ratio 3:5 in July... 22 Jul 2022, 02:49
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The above question is not related to GMAT. Bunuel will you clarify this matter?

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The temperature of Delhi and Lucknow were in the ratio 3:5 in July... 22 Jul 2022, 06:29
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Rev99

Can you please post OA for this question?
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The temperature of Delhi and Lucknow were in the ratio 3:5 in July... 22 Jul 2022, 07:53
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Yes, this is a CAT related question.

yashikaaggarwal
The above question is not related to GMAT. Bunuel[/url] will you clarify this matter?

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The temperature of Delhi and Lucknow were in the ratio 3:5 in July... 22 Jul 2022, 22:27
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Given: 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.

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 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 1/3