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Applied Maths Chapter 3 Solutions
Quantitative Aptitude
EXERCISE- 3.4
Q.1 Ramdin can reap a field in 30 days. What part of the field would he have reaped in 25 days?
Ans. Part of work done by Ramdin in 1 day = 1/30
Part of the work done by Ramdin in 25 days = 1/30 x 25
= 5/6th
Q.2 A farmer can reap a field in 10 days while his wife can do it in 8 days (she does not waste time smoking). If they work together, in how much time can they reap the field?
Ans. Part of work done by a farmer in 1 day = 1/10
Part of work done by wife in 1 day = 1/8
Part of work done by both in 1 day = 1/10 + 1/8
= (4 + 5)/40
= 9/40
Therefore, Time Taken by both = 40/9
= 4 4/9 days
Q.3 A can do a job in 10 days while B can do it in 15 days. If they work together and earn Rs.3500, how should they share the money?
Ans. A’s one day work = 1/10
B’s one day work = 1/15
Ratio of A & B,
A/B = (1/10)/(1/15
A/B = 15/10
= 3/2
A’s share = 3/5 x 3500 = Rs.2100
B’s share = 2/5 x 3500 = Rs.1400
Therefore,
A gets = Rs.2100
B gets = Rs.1400
Q.4 A and B together can paint a room in 2 days. A alone can do it in 3 days. How many days would B require working alone to paint the room?
Ans. (A + B)’s one day work = 1/2
A’s one day work = 1/3
B’s one day work = 1/2 – 1/3
= 1/6
Therefore, B can do the work in 6 days.
Q.5 A can do 1/5th of a certain work in 2 days and B can do 2/3rd of it in 8 days. In how much time can they together complete the work?
Ans. A’s one day work = (1/5)/2 = 1/10
B’s one-day work = (2/3)*8 = 2/(3 x 8) = 1/12
(A & B)’s one day work = 1/10 + 1/12
= (6 + 5)/60
= 11/60
They can do work on 60/11 days
i.e 5 5/11 days
Q.6 One tap fills a tank in 20 minutes and another tap fills it in 12 minutes. The tank is empty and if both taps are opened together, in how many minutes the tank will be full?
Ans. Work done by tap 1 in 20 mins = 1 full tank
T1’s 1 min work = 1/20
Work done by tap 2 in 12 min = 1 full tank
T2’s 1 min work = 1/12
Let, the time taken by 2 taps together be x min
Combined 1 min work = 1/x
1/20 + 1/12 = 1/x
(3 + 5)/60 = 1/x
8/60 = 1/x
x = 60/8
Therefore,
x =7.5 mins.
Q.7 A can do a work in 6 days and B can do it in 8 days. They worked together for 2 days and then B left the work. How many days will A require to finish the work?
Ans. (A & B)’s one day work = 1/6 + 1/8
= (4 + 3)/24
= 7/24
(A & B)’s two days work = 7/24 x 2
= 7/12
Remaining work = 1 – 7/12
= 5/12
A can do 1 work in 6 days
A can-do 5/12 work in = 6 x 5/12
= 2 1/2 days.
Q.8 A can do a piece of work in 40 days. He works at it for 8 days and then B finishes the remaining work in 16 days. How long will they take to complete the work if they do it together?
Ans. A’s one day work = 1/40
A’s eight days work = 1/40 x 8 = 1/5
Remaining work = 1 / 1/5 = 4/5
B’s one day work = (4/5)/16
= 4/(5 x 16)
= 1/20
(A & B)’s one day work = 1/40 + 1/20
= 3/40
Therefore,
Time Taken = 40/3 = 13 1/3 days
Q.9 A and B separately do work in 10 and 15 days respectively. They worked together for some days and then A completed the remaining work in 5 days. For how many days had A and B worked together?
Ans. (A & B)’s one day work = 1/10 + 1/15
= (3 + 2)/30
= 5/30 = 1/6
(A & B)’s x days work = x X 1/6
= X/6
Remaining work = 1 – x/6
= (6 – x)/6
A’s one day work = (6 – x/6)/5
= (6 – x)/30
1/10 = (6 -x )/30
3 = 6 – x
x = 3
Q.10 If 3 women or 5 girls take 17 days to complete a piece of work, how long will 7 women and 11 girls working together take to complete the work?
Ans. Given,
3 Women = 5 Girls
So, 1 Women = 5/3 Girls
ATQ,
Women and Girls working together,
7 Women + 11 Girls
7 x 5/3 Girls + 11 Girls
[(35 + 33)/3] Girls
68/3 Girls
Now,
5 Girls one-day work = 1/17
1 Girls one day work = 1/(17 x 5) = 1/18
68/3 Girls one day work = (1/85) x (68/3)
= 4/15
Time Taken = 15/ 4
Therefore, =3 3/4 days.
Q.11 A, B, and C can separately do work in 2, 6, and 3 days respectively. Working together, how much time would they require to do it? If the work earns them ₹960, how should they divide the money?
Ans. A’s work = 1/2
B’s work = 1/6
C’s work = 1/3
Therefore,
1/2 + 1/6 + 1/3
(3 + 1 + 2)/6 = 6/6 = 1
So, Time Taken = 1 day.
Taking the ratio,
A: B: C = 1/2: 1/6: 1/3
= 3/6: 1/6: 2/6
= 3: 1: 2
A’s share = 3/6 x 960 = Rs.480
B’s share = 1/6 x 960 = Rs.160
C’s share = 2/6 x 960 = Rs.320
Q.12 A, B, and C together can do a piece of work in 15 days, B alone can do it in 30 days and C alone can do it in 40 days. In how many days will A alone do the work?
Ans. Combined one day work = 1/15
B’s one day work = 1/30
C’s one day work = 1/40
A’s one day work = 1/x
According to the question,
1/x + 1/30 x 1/40 = 1/15
1/x + 7/120 = 1/15
1/x = 1/15 – 7/120
1/x = (8 – 7)/120
1/x = 1/120
Therefore,
x = 120 days
Q.13 Navya is twice as efficient as Niti. If they take 10 days to finish a certain job together, how much time will they take individually to finish the same job?
Ans. Let the time Taken by Navya to complete the work be x days
Therefore, according to the question,
Time Taken by Niti alone to complete the work be 2x days
Combined one-day work: 1/10
Navya’s one-day work = 1/x
Niti’s one-day work = 1/2x
1/x + 1/2x = 1/10
(2 + 1)/20 = 1/10
3 x 10 = 2x
30 = 2x
30/2 = x
x = 15 days
Hence, Navya = 15 days
Niti = 30 days
Q.14 A is three times as efficient as B. Also A takes 30 days less than B for doing a piece of work. Find the time taken by them if they work (i) individually and (ii) together.
Ans. Let, Time Taken by A alone be x days
Time Taken by B alone be 3x days
A’s one day work = 1/x
B’s one day work = 1/3x
Combined one day work = 1/p
B – A = 30
3x – x = 30
2x = 30
x = 15 days
(i) Individual work done
A’s Time = 15 days
B’s Time = 45 days
(ii) Work done together
1/15 + 1/45 = 1/p
(3 + 1)/45 = 1/p
4/45 = 1/p
p = 45/4 = 11 1/4 days
Q.15 A is 30% more efficient than B. How much time will they take working together to complete a job that A alone could have done in 23 days?
Ans. Let, the ratio of A & B’s time taken to = 100: 130
= 10: 13
A can do a work in 23 days
B can do work in 13/10 x 23
= 299/10 days
Let, combined one day work = 1/x
A’s one day work = 1/23
B’s one day work = 1/(299/10)
= 10/299
1/23 + 10/299 = 1/x
(13 + 10)/299 = 1/x
23/299 = 1/x
1/13 = 1/x
Therefore,
x = 13 days
Q.16 A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together they can finish the work in 2 days. Find the number of days in which A, B, or C can finish the work alone.
Ans. Let, Time Taken by A alone be 6p days
So, Time taken by B = 3p
Time Taken by C = 2p
Therefore,
A’s one day work = 1/6p
B’s one day work = 1/3p
C’s one day work = 1/2p
Combined one day of work = 1/2
(1/6p) + (1/3p) + (1/2p) = 1/2
(1 + 2 + 3)/6p = 1/2
6/6p = 1/2
1/p = 1/2
Therefore, p = 2 days
A’s alone work = 6p = 6 x 2 = 12 days
B’s alone work = 3p = 3 x 2 = 6 days
C’s alone work = 2p = 2 x 2 = 4 days
Q.17 A pipe can fill a tank in 12 hours. By mistake, a waste pipe at the bottom is left open and the tank is filled in 16 hours. If the tank is full, how much time will the waste pipe take to empty it?
Ans. Let the time required to empty the tank be x hrs.
Filling pipe in 1 hr work = 1/12
Waste pipe’s 1 hr work = 1/x
Combined 1 hr work = 1/16
ATQ,
1/12 – 1/x = 1/16
1/12 – 1/16 = 1/x
(4 – 3)/48 = 1/x
1/48 =1/-x
x = 48
Therefore,
x = 48 hrs.
Q.18 If 4 goats or 6 sheers can graze a held in 40 days, how many days will 4 goats and 14 sheep take to graze the same field?
Ans.
Let, the no. of days be x
4 goats can graze the field in 40 days; so it would take 1 goat 4 x 40 = 160 days.
So, 1 goat grazes the field in 1 day = 1/160
6 sheep can graze the field in 40 days; so it would take 1 sheep 40 x 6 = 240 days.
So, 1 sheep graze the field in 1 day = 1/240
Now,
[(4 x 1/160) + (4 x 1/240)] x = 1
1/40 + 7/120 = 1/x
(3 + 7)/120 = 1/x
10/120 = 1/x
1/12 = 1/x
Therefore,
x = 12 days
Q.19 One tap can fill a tank in 20 hours, while the other can empty it in 30 hours. The tank is empty and both taps are opened together, how long will it take for the tank to be half full?
Ans. Let the time taken to fill the tank with both taps open be x hrs
So, Tank filled in 1 hr = 1/x
1/20 – 1/30 = 1/x
(3 – 2)/60 = 1/x
1/60 = 1/x
x = 60
Therefore,
The time required to fill the tank is 60 hrs
The time required to half-fill the tank would be 30 hrs.
FAQ’s related to Applied Maths Chapter 3 on Quantitative Aptitude:
Q.1 Why is Quantitative Aptitude important?
Ans. Quantitative aptitude skills are crucial for various competitive exams, entrance tests, and job interviews. They are also essential for everyday tasks such as budgeting, financial planning, and decision-making.
Q.2 What topics are covered in Applied Maths Chapter 3?
Ans. Applied Maths Chapter 3 on Quantitative Aptitude typically covers topics such as percentages, profit and loss, clock, time and distance, time and work, averages, ratio and proportion, etc.
Q.3 How will mastering Chapter 3 help you in future exams?
Ans. Mastering Chapter 3 will provide you with a strong foundation in quantitative aptitude, which is essential for scoring well in various competitive exams such as GRE, GMAT, SAT, CAT, banking exams, etc. These exams often contain sections dedicated to quantitative aptitude, and a good score in these sections can significantly enhance your overall performance.
These are few Frequently Asked Questions relating to Applied Maths Chapter 3
In Applied Maths chapter 3, you will explore fascinating topics that form the backbone of practical problem-solving techniques. Through clear explanations, illustrative examples, and step-by-step solutions, you’ll grasp complex concepts effortlessly. Whether you’re preparing for exams or simply eager to deepen your mathematical understanding, Applied Maths Chapter 3 promises an enriching learning experience that will set you on the path to success. Applied Maths Chapter 3, we delve deep into advanced mathematical concepts that are crucial for understanding.
