AP Board 8th Class Maths Solutions Chapter 5 Comparing Quantities Using Proportion Ex 5.1

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 5 Comparing Quantities Using Proportion Ex 5.1 Textbook Questions and Answers.

AP State Syllabus 8th Class Maths Solutions 5th Lesson Comparing Quantities Using Proportion Exercise 5.1

Question 1.
Find the ratio of the following
(i) Smita works in office for 6 hours and Kajal works for 8 hours in her office. Find the
ratio of their working hours.
Solution:
The ratio of working hours of smita and kajal = 6:8
= (2 × 3 ) : (2 × 4) = 3 : 4

(ii) One pot contains 8 litre of milk while other contains 750 milliliter.
Solution:
8lit : 750ml
8 × 1000 : 750
= \([latex]\frac { 8000 }{ 750 }\)[/latex] = 32 : 3

(iii) speed of a cycle is 15km/h and speed of the scooter is 30km/h.
Solution:
The ratio of speeds of a cycle and a sector
= 15 : 30 = (15 × 1) : 15 × 2 = 1 : 2

Question 2.
If the compound ratio of 5:8 and 3:7 is 45:x. Find the value of x.
Solution:
The compound ratio of 5:8 and 3:7
= \(\frac{5}{8} \times \frac{3}{7}=\frac{15}{56}\)
According to the sum
15 : 56 = 45 : x
∴ x = 168

Question 3.
If the compound ratio of 7:5 and 8:x is 84:60. Find x.
Solution:
The compound ratio of 7:5 and 8:x
= \(\frac{7}{5} \times \frac{8}{x}=\frac{56}{5 x}\)
According to the sum
56 : 5x = 84 : 60

∴ x = 8

Question 4.
The compound ratio of 3:4 and the inverse ratio of 4:5 is 45:x. Find x.
Solution:
The inverse ratio of 4:5 is 45 : x
The compound ratio of 3:4 and 5 : 4
= 45 : x

⇒ x = 16 × 3 = 48
∴ x = 48

Question 5.
In a primary school there shall be 3 teachers to 60 students. If there are 400 students
enrolled in the school, how many teachers should be there in the school in the same ratio?
Solution:
No. of teachers are required for 400 students at the rate of 3 teachers to 60
students are ⇒ 60 : 3 400 : x

∴ x = 20

Question 6.
In the given figure, ABC is a triangle. Write all possible ratios by A
taking measures of sides pair wise.
8cm 10cm
(Hint: Ratio of AB : BC =8 : 6)

Solution:

In ΔABC
AB : BC = 8 : 6 = 4:3
⇒ BC : AB = 6 : 8 = 3: 4
BC : CA = 6 : 10 = 3 : 5
⇒ CA : BC = 10 : 6 = 5 : 3
CA : AB = 10:8=5:4
⇒ AB : CA = 8: 10 = 4: 5

Question 7.
If 9 out of 24 students scored below 75% marks in a test. Find the ratio of student scored below 75% marks to the student scored 75% and above marks.
Solution:
Out of 24 students who got below 75% of marks = 9
Who got 75% and above marks =24 – 9 = 15
∴ The ratio between no. of students
who got less than 75% of marks and
who got 75% and above marks
= 9 : 15 =(3 × 3):(3 × 5) = 3 : 5

Question 8.
Find the ratio of number of vowels in the word’ MISSISSIPPI’ to the number of consonants in the simplest form.
Solution:
No. of vowels in the word MI S S SS! PPI = 4 (IIII)
No. of consonants in that word = 7 (MSSSSPP)
∴ The ratio between vowels and consonants = 4: 7

Question 9.
Rajendra and Rehana own a business. Rehana receives 25% of the profit in each month. If
Rehana received ₹ 2080 in particular month, what is the total profit in that month?
Solution:
Total Profit = x say
25% of x = 2080
⇒ \(\frac{25}{100}\) × x = 2080
⇒ \(\frac{x}{4}\) = 2080
⇒ x = 2080 × 4
∴ x = ₹ 8320

Question 10.
In triangle ABC, AB = 2.2 cm, BC = 1.5 cm and AC = 2.3 cm. In triangle XYZ, XY = 4.4cm, YZ = 3cm and XZ = 4.6cm. Find the ratio AB:XY, BC:YZ, AC:XZ. Are the lengths of corresponding sides of ΔABC and ΔXYZ are in proportion?
[Hint : Any two triangles are said to be in proportion, if their corresponding sides are in the
same ratio]
Solution:

∴ The corresponding sides of both the triangles are in proportion.
∴ ΔABC ~ ΔXYZ

Question 11.
Madhuri went to a super market. The price changes are as follows. The price of rice reduced by 5% jam and fruits reduced by 8% and oil and dal increased by 10%. Help Madhuri to find the changed prices in the given table.

Solution:

Question 12.
There were 2075 members enrolled in the club during last year. This year enrolment is
decreased by 4%.
(a) Find the decrease in enrolment.
(b) How many members are enrolled during this year?
Solution:
No. of persons are enrolled in the last year = 2075
Present year no. of persons are enrolled
= 4% less than the previous year.
a) Decrease in enrolment = 4% of 2075

b) No.of members are enrolled this
year = 2075 – 4% of 2075
=2075 – 83 = 1992

Question 13.
A farmer obtained a yielding of 1720 bags of cotton last year. This year she expects her crop to be 20% more. How many bags of cotton does she expect this year?
Solution:
During the last year yielding the bags of
cotton = 1720
If she expects 20% crop to be more then
=20% of 1720 .
= \(\frac{20}{100}\) × 1720
= 2 × 172
= 344 bags
Her expectation of total bags
= 1720 + 344
= 2064

Question 14.
Points P and Q are both in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2: 3, and Q divides AB in the ratio 3 :4. If PQ =2, then find the length of the line segment AB.
Solution:
Given that ‘C’ is the midpoint of line segment AB.
Here ‘P’ divides AB inthe ratio 2 : 3
‘Q’ divides AB in the ratio 3: 4

PQ =2 cm [Given]
PQ = QB – PB
= 4 – 3 = 1 part = 2cm
∴ AB = AQ + QB [with respect to Ql
AB = AP+ PB [with respect to P]
L.C.M. of 5, 7 parts = 35 parts
∴ Length of AB 35 parts
= 35 × 2[ ∵ part = 2cm]
= 70cm