ML Aggarwal Direct and Inverse Variation Exe-9.3 Class 8 ICSE Ch-9 Maths Solutions. We Provide Step by Step Answer of Exe-9.3 Questions for Direct and Inverse Variation as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-8.
ML Aggarwal Direct and Inverse Variation Exe-9.3 Class 8 ICSE Maths Solutions
| Board | ICSE |
| Publications | Avichal Publishig Company (APC) |
| Subject | Maths |
| Class | 8th |
| Chapter-9 | Direct and Inverse Variation |
| Writer | ML Aggarwal |
| Book Name | Understanding |
| Topics | Solution of Exe-9.3 Questions |
| Edition | 2023-2024 |
Direct and Inverse Variation Exe-9.3
ML Aggarwal Class 8 ICSE Maths Solutions
Page-161
Question 1. A farmer can reap a field in 10 days while his wife can do it in 8 days (she does not waste time in smoking). If they work together, in how much time can they reap the field?
Answer:
A farmer can reap a field in = 10 days
In 1 day farmer can reap field = 1/10 days
The farmer’s wife can reap a field in = 8 days
In 1 day farmer’s wife can reap field = 1/8 days
Both farmer and his wife can reap field in 1 day = 1/10 + 1/8
= (4+5)/40
= 9/40
So, Farmer and his wife reap field in 40/9 days i.e. 4 4/9 days.
Question 2. 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?
Answer:
A can do 1/5th of a certain work in = 2 days
So, A’s, 1 day work = 1/5 × 1/2 = 1/10
B can do 2/3rd of a certain work in = 8 days
So, B’s, 1 day work = 2/3 × 1/8 = 1/12
(A + B)’s 1 day work = 1/10 + 1/12
= (6+5)/60
= 11/60
∴ (A + B) can do the complete work in = 1/(11/60) days
= 60/11 days
= 5 5/11 days
Question 3. One tap fills a tank in 20 minutes and another tap fills it in 12 minutes. The tank being empty and if both taps are opened together, in how many minutes the tank will be full?
Answer:
First tap fill a tank in 20 minutes
Second tap fill a tank in 12 minutes
In 1 minute first tank fills = 1/20 parts
In 1 minute 2nd tank fills = 1/12 parts
In 1 minute both 1st and 2nd tank fills = 1/20 + 1/12
= (3+5)/60
= 8/60 parts
= 2/15 parts
∴ Both first and 2nd tank fills in = 1/(2/15) minutes
= 15/2 minutes
= 7 ½ minutes
Question 4. 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?
Answer:
A can do a work in = 6 days
A’s, 1 day work = 1/6
B can do a work in = 8 days
B’s, 1 day work = 1/8
Both (A+B)’s 1 day work = 1/6 + 1/8
= (4+3)/24
= 7/24
Both (A+B)’s 2 day work = 2 × (7/24)
= 7/12
So, the remaining work = 1 – 7/12
= (12-7)/12
= 5/12
Now,
It is given that, A can do a work in = 6 days
A can do 5/12 work in = 6 × (5/12) days
= 5/2 days
= 2 ½ days
So, A can finish the work in 2 ½ days.
Question 5. 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?
Answer:
A can do a piece of work in = 40 days
A’s, 1 day work = 1/40
A’s, 8 day work = 8/40 = 1/5
Remaining work = 1 – 1/5
= (5-1)/5
= 4/5
B can do 4/5 piece of work in = 16 days
B’s, 1 day work = (4/5)/16
= 4/(5×16)
= 1/20
Now, (A+B)’s 1 day work = 1/40 + 1/20
= (1+2)/40
= 3/40
∴ Both (A+B) can do a piece of work in = 1/(3/40) days
= 40/3 days
= 13 1/3 days
Direct and Inverse Variation Exe-9.3
ML Aggarwal Class 8 ICSE Maths Solutions
Page-162
Question 6. A and B separately do a work in 10 and 15 Solution: 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?
Answer:
A can do a work in = 10 days
B can do a work in = 15 days
A’s, 1 day work = 1/10 …. (1)
B’s, 1 day work = 1/15
(A + B)’s 1 day work = 1/10 + 1/15
= (3+2)/30
= 5/30
= 1/6
let us consider (A+B) worked together for ‘x’ days.
So, (A+B)’s, x day work = x/6
Remaining work = 1 – x/6
A can do the remaining work, (1 – x/6) in = 5 days
So, A’s 1 day work = (1 – x/6)/5
= (6 – x)/(6×5)
= (6 – x)/30 ….. (2)
From (1) and (2), we get
1/10 = (6 – x)/30
30/10 = 6 – x
3 = 6 – x
x = 6 – 3
= 3
So, Both A and B can do work together in 3 days.
Question 7. 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?
Answer:
3 women’s work = 5 girl’s work
1 women’s work = 5/3 girl’s work
7 women’s work = (5/3) × 7 girl’s work = 35/3 girls’ s work
7 women and 11 girls works = (35/3) + 11 girl’s work = 68/3 girl’s work
Since 5 girls can do the work in 17 days
1 girl can do the work in = 17 × 5 days
68/3 girls can do the work in = (17 × 5)/(68/3) days
= (17 × 5 × 3)/68 days
= 15/4 days
= 3 ¾ days
So, 7 women and 11 girls can do the complete work in 3 ¾ days.
Question 8. A can do a job in 10 days while B can do it in 15 days. If they work together and earn ₹3500, how should they share the money?
Answer:
A can do a job in = 10 days
A’s 1 day job is = 1/10
B can do a job in 15 days
B’s 1 day job is = 1/15
Both A and B can do job in one day = 1/10 + 1/15
= (3+2)/30
= 5/30
= 1/6
For 1/6 part of work the earnings is = ₹3500
For 1 part of work the earnings is = ₹3500 × 6
For 1/10 part of work earning = ₹ (3500×6)/10 = ₹2100
For 1/15 part of work earning = ₹ (3500×6)/15 = ₹1400
∴ A gets ₹2100 and B gets ₹ 1400
Question 9. A, B and C can separately do a work in 2, 6 and 3 days respectively. Working together, how much time would they require to do it? If the work earns them ₹1960, how should they divide the money?
Answer:
A’s one day work = ½
B’s one day work = 1/6
C’s one day work = 1/3
A + B + C when working together = ½ + 1/6 + 1/3
= (3 + 1 + 2)/6
= 6/6
= 1day
∴ A, B and C can finish the work by working together in 1 day.
So they should divide the money in the ratio 1/2 : 1/6 : 1/3
(½) × 12 : (1/6) × 12 : (1/3) × 12 = 6: 2: 4
So, sum of terms of ratio = 6 + 2 + 4 = 12
∴ A’s share = (6/12) × ₹960
= ₹480
B’s share = (2/12) × ₹960
= ₹160
C’s share = (4/12) × ₹960
= ₹320
Question 10. 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?
Answer:
(A + B + C) can do a piece of work in = 15 days
(A + B + C)’s 1 day work = 1/15
B alone can do a piece of work in = 30 days
B’s 1 day work = 1/30
C alone can do a piece of work in = 40 days
C’s 1 day work = 1/40
So, A’s 1 day work = (1/15) – [1/30 + 1/40]
= (1/15) – [(4+3)/120]
= (1/15) – (7/120)
= (8-7)/120
= 1/120
∴ A can do a piece of work in = 120 days.
Question 11. A, B and C working together can plough a field in 44⁄5 days. A and C together can do it in 8 days. How long would B working alone take to plough the field?
Answer:
(A + B + C) can plough a field in = 4 (4/5) days = 24/5 days
(A + B + C)’s 1 day work = 5/24 days
(A + C) can plough a field in = 8 days
(A + C)’s 1 day work = 1/8 days
B’s 1 day work = (5/24) – 1/8
= (5-3)/24
= 2/24
= 1/12
∴ B can do the work in 12 days.
ML Aggarwal Direct and Inverse Variation Exe-9.3 Class 8 ICSE Maths
Question 12. A and B together can build a wall in 10 days; B and C working together can do it in 15 days; C and A together can do it in 12 days. How long will they take to finish the work, working altogether? Also find the number of days taken by each to do the same work, working alone.
Answer:
(A + B)’s can build a wall in = 10 day
(A + B)’s 1 day work = 1/10
(B + C)’s can build a wall in = 15 days
(B + C)’s 1 day work = 1/15
(C + A)’s can build a wall in = 12 days
(C + A)’s 1 day work = 1/12
[(A+B) + (B+C) + (C+A)]’s 1 day work = 1/10 + 1/15 + 1/12
2 (A+B+C)’s 1 day work = (6 + 4 + 5)/60
= 15/60
= ¼
(A+B+C)’s 1 day work = 1/(2×4)
= 1/8
So, (A+B+C) can build the wall in = 8 days
Now let us find the number of days taken by each to do the same work, working alone:
=>Also, [(A+B+C) – (B + C)]’s 1 day work = 1/8 – 1/15
= (15 – 8)/120
= 7/120
A’s 1 day work = 7/120
So, A can build the wall in = 120/7 days
= 17 1/7 days
=>Also, [(A+B+C) – (A + C)]’s 1 day work = 1/8 – 1/12
= (3 – 2)/24
= 1/24
B’s 1 day work = 1/24
So, B can build the wall in = 24 days
=>Also, [(A+B+C) – (A + B)]’s 1 day work = 1/8 – 1/10
= (5 – 4)/40
= 1/40
C’s 1 day work = 1/40
So, C can build the wall in = 40 days
∴ A can complete the work in 17 1/7 days.
B can complete the work in 24 days.
C can complete the work in 40 days.
Question 13. A pipe can fill a tank in 12 hours. By mistake, a waste pipe in the bottom is left opened and the tank is filled in 16 hours. If the tank is full, how much time will the waste pipe take to empty it?
Answer:
— End of Direct and Inverse Variation Exe-9.3 Class 8 ICSE Maths Solutions :–
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