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

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#### 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?

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?

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?

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?

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?

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

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#### 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?

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?

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?

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?

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?

(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?

(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.

(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.