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 :
$$\frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}}$$
M1 = No. of men
D1 = No .of days
W1 = Cost of rice
∴ M1 = 8
D1 = 20
W1 = ₹ 480
M2 = 12
D2 = 15
W2 = ? (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:
$$\frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}}$$
∴ M1 = 10
D1 = 5
W1 = 75
M2 = 15
D2 = ?
W2 = 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:
M1D1H1 = M2D2H2
∴ M1 = 24
D1 = 15 days
H1 = 8 hrs
M2 = 20
D2 = ?
H2 = 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:
$$\frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}}$$
M1 = 175
D1 = 36
W1 = 3150
M2 = ?
D2 = 24
W2 = 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:
M1D1H1 = M2D2H2
M1 = 14
D1 = 12 days
H1 = 6
M2 = 4
D2 = ?
H2 = 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]