# an air conditioner can cool the hall in 40 minutes while another takes 60 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?

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## An air conditioner can cool the hall in 40 minutes while another takes 45 minutesto cool under similar conditions. If both air conditioners are switched on at the same instance then how long will it take to cool the room approximately?

An air conditioner can cool the hall in 40 minutes while another takes 45 minutesto cool under similar conditions. If both air conditioners are switched on at the same instance then how long will it take to cool the room approximately?

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An air conditioner can cool the hall in 40 minutes while another takes 45 minutesto cool under similar conditions. If both air conditioners are switched on at the same instance then how long will it take to cool the room approximately?

Question

An air conditioner can cool the hall in

40 minutes while another takes 45 minutes

to cool under similar conditions. If both air conditioners are switched on at the same instance then how long will it take to cool the room approximately?

A 18 min B 19 min C 22 min D 24 min Open in App Solution

The correct option is **C**

22 min

**Correct option: (c )**

22 min

Let the two conditioners be

A and B Air conditioner A cools at 40 minutes Air conditioner B at 45 minutes We know that,

capacity=1time taken to cool the hall

We have, The capacity of A=140 and capacity of B=145

So, when both the air conditioners are turned on at the same time, the combined capacity will be the addition of the capacity of both the air conditioners.

So, the combined capacity of

A and B is 140+145=45+4040×45 Now, we know that

Time taken =1combined capacity

= (45 x 45)45+40 = 180045= 21.1764 = 22 min (approximately).

The air conditioner A and air conditioner B

together take approximately

22 min to cool the room.

Hence, option C is correct.

Suggest Corrections 1

SIMILAR QUESTIONS

**Q.**

Noah noticed that an air conditioner from Company A can cool a hall in 10 minutes, while an air conditioner from Company B can do the same in 15 miutes.

It is a very hot day, so Noah has turned on both the air conditioners.

Find how long both the air conditioners will take to cool the hall.

## An air conditioner can cool the hall in 40 miutes

Time and Work Questions & Answers for GRE,GATE,CAT,Bank Exams,AIEEE, Bank PO,Bank Clerk : An air conditioner can cool the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. If both air conditioners are switch

117 Q:

An air conditioner can cool the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room approximately ?

A) 18 minutes B) 19 minutes

C) 22 minutes D) 24 minutes

Answer: C) 22 minutes

Explanation:

Let the two conditioners be A and B

'A' cools at 40min 'B' at 45min

Together = **(a x b)/(a + b)**

= (45 x 40)/(45 + 40)

= 45 x 40/85 = 21.1764 = **22 min** (approx).

Subject: Time and Work - Quantitative Aptitude - Arithmetic Ability

Exam Prep: GRE , GATE , CAT , Bank Exams , AIEEE

Job Role: Bank PO , Bank Clerk

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## An air conditioner can cool the hall in $40$ minutes while another takes $45$ minutes to cool under similar conditions. If both air conditioners are switched on at the same time then how long will it take to cool the room approximately?(A) $18$ minutes (B) $19$ minutes (C) $22$ minutes (D) $24$ minutes

An air conditioner can cool the hall in $40$ minutes while another takes $45$ minutes to cool under similar conditions. If both air conditioners are switched on at the same time then how long will it take to cool the room approximately?(A) $18$ minut...

An air conditioner can cool the hall in40 40

minutes while another takes

45 45

minutes to cool under similar conditions. If both air conditioners are switched on at the same time then how long will it take to cool the room approximately?

(A) 18 18 minutes (B) 19 19 minutes (C) 22 22 minutes (D) 24 24 minutes Answer Verified 161.4k+ views

**Hint:**To solve the problem, air conditioners have capacity, which is the inverse of time taken by it to cool the hall, that means,

Capacity = 1

Time taken to cool the hall

Capacity = 1Time taken to cool the hall

So, when both the air conditioners are turned on at the same time, the combined capacity will be the addition of the capacity of both the air conditioners. So, the time will required will be the reciprocal of the combined capacity, that means,

Time required = 1 Combined Capacity

Time required = 1Combined Capacity

**Complete answer:**Let the first air conditioner be named A and the second air conditioner be named B.

Given, time taken by A to cool the hall,

T A =40 TA=40 minutes

And, time taken by B to cool the hall

T B =45 TB=45 minutes

Now, the capacity of A,

C A = 1

Time taken by A to cool

= 1 T A

CA=1Time taken by A to cool=1TA

⇒ C A = 1 40 ⇒CA=140

And, the capacity of

B B , C B = 1

Time taken by B to cool

= 1 T B

CB=1Time taken by B to cool=1TB

⇒ C B = 1 45 ⇒CB=145

Now, when the two air conditioners are switched on at the same instance, both

A A and B B

together cool the room.

Therefore, the combined capacity of A and B,

C A+B = C A + C B −−−(1) CA+B=CA+CB−−−(1)

Now, substituting the values of

C A CA and C B CB in equation (1) (1) , ⇒ C A+B = 1 40 + 1 45 ⇒CA+B=140+145

Taking LCM of the denominators, we get,

⇒ C A+B = 45+40 40×45 ⇒CA+B=45+4040×45

Simplifying the fraction, we get,

⇒ C A+B = 85 1800 ⇒CA+B=851800

Cancelling the common factors in numerator and denominator, we get,

⇒ C A+B = 17 360 ⇒CA+B=17360

Therefore, the time required to cool the room by both A and B,

T A+B = 1 Combined Capacity = 1 C A+B

TA+B=1Combined Capacity=1CA+B

⇒ T A+B = 1 17 360 ⇒TA+B=117360 ⇒ T A+B = 360 17 ⇒TA+B=36017

Simplifying the calculations, we get,

⇒ T A+B =21.176 ⇒TA+B=21.176 ⇒ T A+B ≈22 ⇒TA+B≈22

minutes (approximately)

Therefore, the combined time required by the two air conditioners is

22 22 minutes.

**Hence, the correct answer is option (C).**

**Note:**

The other approach to this problem is by unitary method, in which we are to find how much each air conditioner cools in

1 1

minute. Then we find how much the two air conditioners can cool in

1 1

minute together. Then, finding the reciprocal of how much the two air conditioners cool together, we get the required time in which both the air conditioners cool the room. We must take care of calculations as the question involves tedious calculative steps.

Guys, does anyone know the answer?