AP State Syllabus AP Board 8th Class Maths Solutions Chapter 10 Direct and Inverse Proportions Ex 10.4 Textbook Questions and Answers.

## AP State Syllabus 8th Class Maths Solutions 10th Lesson Direct and Inverse Proportions Exercise 10.4

Question 1.

Rice costing ₹480 is needed for 8 members for 20 days. What is the cost of rice required for 12 members for 15 days?

Solution:

Method – 1: Number of men and rice required to them are in inverse proportion.

Number of men ∝ \(\frac{1}{\text { No. of days }}\)

⇒ Compound ratio of 8:12 and 20: 15

= \(\frac{8}{12}=\frac{20}{15}\) = \(\frac{8}{9}\) …………….. (2)

From (1), (2)

480 : x = 8 : 9

⇒ \(\frac{480}{x}=\frac{8}{9}\)

⇒ x = \(\frac{480 \times 9}{8}\) = ₹540

∴ The cost of required rice is ₹ 540

Method – II :

\(\frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}}\)

M_{1 }= No. of men

D_{1} = No .of days

W_{1} = Cost of rice

∴ M_{1} = 8

D_{1} = 20

W_{1} = ₹ 480

M_{2} = 12

D_{2} = 15

W_{2} = ? (x)

⇒ x = 45 x 12 = ₹ 540

The cost of required rice = ₹ 540/-

Question 2.

10 men can lay a road 75 km. long in 5 days. In how many days can 15 men lay a road 45 km. long?

Solution:

\(\frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}}\)

∴ M_{1} = 10

D_{1} = 5

W_{1} = 75

M_{2} = 15

D_{2} = ?

W_{2} = 45

∴ x = 2

∴ No. of days are required = 2

Question 3.

24 men working at 8 hours per day can do a piece of work in 15 days. In how many days can 20 men working at 9 hours per day do the same work?

Solution:

M_{1}D_{1}H_{1} = M_{2}D_{2}H_{2}

∴ M_{1} = 24

D_{1} = 15 days

H_{1} = 8 hrs

M_{2} = 20

D_{2} = ?

H_{2} = 9 hrs

⇒ 24 × 15 × 8 = 20 × x × 9

∴ No. of days are required = 16

[ ∵ No. of men and working hours are in inverse]

Question 4.

175 men can dig a canal 3150 m long in 36 days. How many men are required to dig a canal 3900 m. long in 24 days?

Solution:

\(\frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}}\)

M_{1} = 175

D_{1} = 36

W_{1} = 3150

M_{2} = ?

D_{2} = 24

W_{2} = 3900

∴ No. of workers are required = 325

Question 5.

If 14 typists typing 6 hours a day can take 12 days to complete the manuscript of a book, then how many days will 4 typists, working 7 hours a day, can take to do the same job?

Solution:

M_{1}D_{1}H_{1} = M_{2}D_{2}H_{2}

M_{1} = 14

D_{1} = 12 days

H_{1} = 6

M_{2} = 4

D_{2} = ?

H_{2} = 7

⇒ 14 × 12 × 6 = 4 × x × 7

⇒ x = 36

∴ No. of days are required = 36

[ ∵ No of men and working hours are in inverse proportion]