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.

Item | Original price/kg | Changed price |

Rice | ₹ 30 | |

Jam | ₹ 100 | |

Apples | ₹ 280 | |

Oil | ₹ 120 | |

Dal | ₹ 80 |

Solution:

Item | Original price/kg | Changed price |

Rice | ₹ 30 | ₹28.50 |

Jam | ₹ 100 | ₹ 92 |

Apples | ₹ 280 | ₹ 257.6 |

Oil | ₹ 120 | ₹ 132 |

Dal | ₹ 80 | ₹ 88 |

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