Frank Learning Maths Class 6 Solutions Chapter 9

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Frank Learning Maths Class 6 Solutions Chapter 9 Ratio and Proportion

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Frank Learning Maths Class 6 Book, Chapter 9 Ratio and Proportion. Here students can easily find step by step solutions of all the problems for Ratio and Proportion. Here students will find solutions for Exercise 9.1, 9.2 and 9.3 and also get solution for Chapter Check-up questions.

Exercise wise proper solutions. All the problem are solved with easily understandable methods so that all the students can understand easily. Here in this post all Mathematic solutions are based on the CBSE latest curriculum.

Ratio and Proportion Exercise 9.1 Solution

Question no – (1)

Solution :

(a) 24 to 96

ratio = 1 : 4

(b) 12 to 48

ratio = 1 : 4

(c) 10 to 30

ratio = 1 : 3

(d) 69 to 23

ratio = 3 : 1

Question no – (2)

Solution :

From the given data,

Ram gave 34 toffees to Meena and 68 to Tina.

Ratio of toffees given to the two.

= 34 : 68

= 1 : 2

Therefore, the ratio of toffees given to the two is 1 : 2

Question no – (3)

Solution :

(a) the number of boys to the number of girls.

= 1800 : 1500

= 6 : 5

(b) the number of boys to the total number of students in the school.

= 1800 : 3300

= 6 : 11

(c) the number of girls to the total number of students in the school.

= 1500 : 3300

= 5 : 11

Question no – (4)

Solution :

As per the given question,

Raju’s father earns 24,000 per month while his mother earns 18,000 per month.

Now, the ratio,

= 24000 : 18000

= 4 : 3

Thus, ratio of money earned by his father to the money earned by his mother is 4 : 3

Question no – (5)

Solution :

According to the question,

40 sweets are to be distributed between Sita and Geeta in the ratio of 7 : 3 ,

Now, Sita will get,

= (40 × 7/10)

= 28 sweets

Gita will get,

= (40 × 3/10)

= 12 sweets

Hence, they each will get Sita 28 sweets and Geeta 12 sweets.

Question no – (6)

Solution :

As per the question,

Express train travels 45 km per hour while a passenger train travels 30 km per hour.

Therefore,

= 45 : 30

= 3 : 2

Hence, the ratio of the speed of the express train to that of the passenger train is 3 : 2

Question no – (7)

Solution :

Given in the question,

A scooter travels 120 km in 3 hours and a train travels 120 km in 2 hours.

First, Speed of scoters

= 120/3

= 40km/hr

Now, Speed of train

= 120/2

= 60 km/hr

ratio of their speed,

= 40 : 60

= 2 : 3

Thus, the ratio of their speeds is 2 : 3

Question no – (8)

Solution :

According to the question,

In an election, candidates A and B received votes in the ratio of 2: 3.

The total number of votes cast was 60.

Candidate A got,

= (60 × 2/5)

= 24 votes

Therefore, candidate A get 24 votes.

Question no – (9)

Solution :

From the question we get,

The marked price of a table is Rs 625 and its sale price is 500.

Therefore,

= 500 : 625

= 4 : 5

Thus, the ratio of the sale price to the marked price is 4 : 5

Question no – (10)

Solution :

(a) AC : AF

= 2 : 5

(b) AG : AD

= 6 : 3

= 2 : 1

(c) BF : AI

= 4 : 8

= 1 : 2

(d) CE : DI

= 2 : 5

Question no – (11)

Solution :

(a) The ratio of car to its wheels.

= 1 : 4

(b) The ratio of hands to fingers.

= 2 : 10

(c) If there are 15 tricycle wheels, how many tricycles are there?

= 15 ÷ 3

= 5 tricycles

(d) If there are 45 fingers, how many hands are there?

= 45/5

= 9 hands

(e) If the ratio of boys to girls in a team is 2 : 3 and there are 18 girls, how many boys are there?

= 18 × 2/3

= 12 boys

Question no – (12)

Solution :

As per the question we know,

3/4 of the letters that Mr. Mahesh gets are bills,

Therefore,

= 3 : (4 – 3)

= 3 : 1

Thus, the ratio of the number of bills to the number of other letter is 3 : 1.

Question no – (13)

Solution :

According to the question,

Saturn and Jupiter take 9 hours 56 minutes and 10 hours 40 minutes, respectively for one spin on their axes.

Therefore,

= {(9 × 60) + 56} (10 × 60) + 40}

= {540 + 6} {600 + 40}

= 596 : 640

= 149 : 160

Thus, the ratio of the time taken by Saturn and Jupiter in lowest form is 149 : 160

Question no – (14)

Solution :

From the question,

An office opens at 9 am and closes at 5 : 30 pm with a lunch break of 30 minutes.

Therefore,

= 30 : {(8 × 60) + 30} 30 : {480 + 30)

= 30 : 510

= 1 : 17

Hence, the ratio of lunch break to the total period in the office is 1 : 17

Question no – (15)

Solution :

Form the given data we know,

Cost of a dozen pens is 180 and cost of 8 ball pens is 56.

First, Cost of pen,

= 180/12

= 15 rupees

Cost of a ball pen,

= 56/8

= 7 rupees

Therefore, their ratio will be 15 : 7

Question no – (16)

Solution :

Ratio of Shreya and Bhoomika’s age,

= 15 : 12

= 5 : 4

Shreya will get,

= (360 × 5/9)

= 200 rupees

Bhoomika will get,

= (360 × 4/9)

= 160 rupees

Question no – (17)

Solution :

(a) Present age of father to the present age of son.

= 42 : 14

= 3 : 1

(b) Age of the father to the age of son, when son was 12 years old.

= (42 – 2) : (14 – 2)

= 40 : 12

= 10 : 3

(c) Age of father after 10 years to the age of son after 10 years.

= (42 + 10) : (14 + 10)

= 52 : 24

= 13 : 6

(d) Age of father to the age of son when father was 30 years old.

= (42 – 12) : (14 – 12)

= 30 : 2

= 15 : 1

Try These 9 (i) :

Question no – (1)

Solution :

(a) Cost of a pencil is 90 paise and that of a pen is Rs 15.

Now,

= 90 paise : (15 × 100) paise

= 90 : 1500

= 3 : 50

Thus, the ratio is 3 : 50

(b) Length of a lizard is 20 cm and that of a crocodile is 4 m.

Now, 20 cm : (4 × 100) cm

= 20 : 400

= 1 : 20

Hence, the ratio is 1 : 20

Try These 9 (ii) :

Question no – (1)

Solution :

(a) 4/9

Two equivalent ratios = 8 : 18, 12 : 27

(b) 5/7

Two equivalent ratios = 10 : 14, 15 : 21

(c) 8/11

Two equivalent ratios = 16 : 22, 24 : 33

(d) 9/13

Two equivalent ratios = 18 : 26, 27 : 39

Question no – (2)

Solution :

From the given ratios, Option – (c) 6 : 3 is not same as 3 : 1

6 : 3

= 2 : 1 ≠ 3 : 1

Question no – (3)

Solution :

From the given ratios i the question option – (c) 30 : 75 is same as 2 : 5.

30 : 75

= 6 : 15

= 2 : 5

Try These 9 (iii) :

Question no – (1)

Solution :

(a) 5/20 = _/4 = 3/_

= 5/20 = 1/4 = 3/12

(b) 13/91 = 1/_= _/455

= 13/91 = 1/7 = 65/455

(c) 16/28 = 4/_= _/35

= 16/28 = 4/7 = 20/35

(d) 9/27 = 3/_= _/36

= 9/27 = 3/9 = 12/36

Question no – (2)

Solution :

Let, the number of boys in my class = 96

And the number of girls = 69

Now, 96 : 69

= 32 : 23

Therefore, the ratio of boys to the number of girls will be 32 : 23

Question no – (3)

Solution :

Let, the the number of doors = 2

To the number of windows = 4

Now, 2 : 4

= 1 : 2

Therefore, the ratio of the number of doors to the number of windows is 1 : 2

Try These 9 (iv) :

Question no – (1)

Solution :

(a) 30 in the ratio of 1 : 2

= (30 × 1/3), (30 × 2/3)

= 10 : 20

(b) 15 in the ratio of 2:1

= (15 × 2/3), (15 × 1/3)

= 10 : 5

(c) 60 in the ratio of 1:3

(60 × 1/4), (60 × 3/4)

= 15 : 45

(d) 6000 in the ratio of 1 : 3

(6000 × 1/4), (6000 × 3/4)

= 1500 : 4500

(e) 1400 in the ratio of 3 : 4

(1400 × 3/7), (1400 × 4/7)

= 600 : 800

Try These 9 (v) :

Question no – (1)

Solution :

(a) 4 : 9 and 3 : 36

= Given ratios are 4/9 and 3/36

LCM of 9 and 36 is 36

4 × 4/9 × 4 = 16/36 and 3/36

Clearly 16/36 > 3/36, i.e 4/9 > 3/36

(b) 8 : 25 and 4 : 50

= Given ratios are 8/25 , 4/50

LCM of 25 and 50 is 50

8 × 2/25 × 2 = 16/50 and 4/50

Clearly, 16/50 > 4/50 i.e, 8/25 > 4/50

(c) 3 : 2 and 9 : 6

= Given ratios are 3/2 and 9/6

LCM of 2 and 6 is 6

3 × 3/2 × 3 = 9/6 and 9/6

3/2 = 9/6

Ratio and Proportion Exercise 9.2 Solution

Question no – (1)

Solution :

(a) 25, 30, 40, 48

= 25 × 48

= 1200 = 30 × 40 (proportion)

(b) 32, 48, 70, 210

= 32 × 210

= 6720 ≠ 48 × 70 (in proportion)

(c) 13, 169, 12, 156

= 13 × 156

= 2028 = 169 × 12 (proportion)

Question no – (2)

Solution :

(a) Given, 80 : 100 : : x : 45

x = 80 × 45/100

or, x = 20

Thus, the missing number is 20

(b) Given, 27 : 15 : : 36 : x

x = 15 × 36/27

or, x = 20

Thus, the missing number is 20.

(c) Given, 64 : 80 : : x : 5

x = 64 × 5/80

x = 4

Hence, the missing number is 4

Question no – (3)

Solution :

(a) 30 cm : 75 cm and 50 m : 125 m

= (30 : 75) and (50 × 100) : (125 × 100) = (2 : 5)

= 30 × 5 = 150

= 75 × 2

The given ratios from proportion

(b) 26 litres : 78 litres and 6 bottles : 12 bottles

= (26 : 78) and (6 : 12)

= (1 : 3) and (1 : 2)

Since, 1 × 2 ≠ 3 × 1

Therefore, the given ratios don’t from proportion

(c) 150 g : 2 kg and 10 seconds : 3 minutes

= (150 : 2 × 1000) and (10 : 3 × 60)

= (3 : 40) and (1 : 18)

= 3 × 18 ≠ 40 × 1

Therefore the given ratios don’t from proportion

Question no – (4)

Solution :

As per the given question,

The ratio of the length of a rectangle to its width is = 5 : 2.

Length of rectangle is = 40 cm,

Let, x cm be the breadth

= (5 : 2) and (40 : x) will from proportion

= 5 × x = 2 × 40

= 2 × 40/5

= 16

Therefore, the width will be 16 cm.

Question no – (5)

Solution :

Given in the question,

The ratio of the length of Ram’s string to that of Shyam’s string is = 2 : 7.

Shyam’s string is = 42 inches long

Let, the length of Ram’s string = x inches

= (2 : 7) and (x : 42) will from proportion

= 2 × 42 = 7 × x

Or, n = 2 × 42/4

= 12 inches

Therefore, Ram’s string is 12 inches long.

Question no – (6)

Solution :

According to the question,

For every three push-ups Andy can do, Sandy does two push-ups.

Andy did nine push-ups during a gym class,

Let, Sandy did x push-ups

= (3 : 2) = 2 × 9

= x = 2 × 9/3

= 6

Therefore, Sandy did 6 push-ups.

Hence, Push-ups they do altogether,

= (9 + 6 ) = 15

Question no  – (7)

Solution :

Let, the opponent received x votes,

= (5 : 7) and (x : 20734) will from proportion

= 7 × x = 5 × 20734

= x = 5 × 20734/7

= x = 14810

Thus, his opponent receive 14810 votes.

Question no – (8)

Solution :

According to the given figure,

= (8 : 18) and (10 : n) will from proportion

= 8 × n = 18 × 10

or, n = 18 × 10/8

n = 225 cm

Therefore, here the n is = 225 cm.

Question no – (9)

Solution :

Acceding to the question,

On a map, 1 cm represents 10 km.

The two towns are actually 130 km apart.

Let, their distance in map be x cm

= (1 : 10) and 9x : 130) will from proportion

= 1 × 130 = 19 × x

or, x = 13 cm

Therefore, they are 13 cm away on the map.

Question no – (10)

Solution :

Given in the question,

On a map, 5 cm represents 600 km.

Two towns are shown 20 cm apart on the map

Let, their actual distance ne x km

= (5 : 60) and (20 : x) will from proportion

= 5 × x = 600 × 20

or, x = 600 × 20/5 = 2400 km

Hence, their actual distance is 2400 km.

Question no – (11)

Solution :

According to the given question,

A metal pipe 3 m long was found to weigh 7.8 kg.

Let, the weight be x kg

= (3 : 7.8) and (8 : x) will from proportion

= 3 × x = 7.8

or, x = 7.8 × 8/30

= 208/10

= 20.8 kg

Therefore, the weight of the same kind of 8 m long pipe will be 20.8 kg.

Question no – (12)

Solution :

(a) How many plants did the worm destroy in the whole field?

= The number of rows

= 1890/63

= 30

In each row, the worm destroyed 10 plants

So, in total the worm destroyed

= (18 × 30)

= 540 plants

(b) What ratio of the plants destroyed to the plants each in row.

= 18 : 63

= 2 : 7

Try These 9 (vi) :

Question no – (1)

Solution :

(a) Given ratios, 6 : 30 and 12 : 60

6 : 30

= 6/30

= 1/5

Now, 12 : 60

= 12/60

= 1/5

Thus, these a ratios are in proportion.

(b) Given ratios, 18 : 45 and 8 : 20

18 : 45

= 18/45

= 2/9

Now, 8 : 20

= 8/20

= 2/5

Hence, these ratios are not in proportion.

(c) Given ratios, 34 : 85 and 25 L 45

34 : 85

= 34/85

= 2/5

Now, 25 : 45

= 25/45

= 5/9

Hence, these ratios are not in proportion.

(d) Given ratios, 28 : 63 and 36 : 81

28 : 63

= 28/63

= 4/9

Now, 36 : 81

= 36/81

= 4/9

Therefore, these ratios are in proportion.

Ratio and Proportion Exercise 9.3 Solution

Question no – (1)

Solution :

Froom the question we get,

A person buys 5 kg of rice for Rs 150.

Let, his payment by x rupees.

(5 : 150) and (20 : x) will from proportion

= 5 × x = 150 × 20

= x = 150 × 20/5

= x = 600 rupees

Thus, he will pay 600 rupees for 20 kg of rice.

Question no – (2)

Solution :

As per the question,

Shyam saves 10,000 rupees in a month

Shyam saves,

= (10,000 × 12)

= 120,000 rupees in a year.

Therefore, annual savings of Shyam will be Rs. 120,000

Question no – (3)

Solution :

The aeroplane moves 600 km in a hour …(According to the question)

The aeroplane moves 1200 km in,

= 1200/600

= 2 hour

If will return to Delhi two hours later to 7 p.m. i.e 9 pm.

Question no – (4)

Solution :

The pipe con fill half of the tank in 2 hours …(according to the question)

The pipe can fill full of the tank in,

= (2 × 5)

= 10 hours

The pipe can fill 5 such tanks in,

= (10 × 5)

= 50 hours

Question no – (5)

Solution :

It has rained 276 mm in 3 days …(according to the question)

It has rained 276/3 = 92 mm in 1 day

= will rain (92 × 7) mm  = 644 mm

Therefore, 64.4 cm of rain will fall in one full week

Question no – (6)

Solution :

Let, Nimit can type x words in 2 minutes

So, (11 : 8) and x : (2 × 60)} will from proportion

11 × 120 = 8 × x

or, x = 11 × 12/8

or, x = 165 words

Therefore, he can type 165 words in 2 minutes.

Question no – (7)

Solution :

Let, Nimit can type x words in 2 minutes

So, (11 : 8) and x : (2 × 60)} will from proportion

11 × 120 = 8 × x

or, x = 11 × 12/8

or, x = 165 words

Therefore, he can type 165 words in 2 minutes.

Question no – (8)

Solution :

Cost of 5 kg of wheat is ₹ 30.50. …(according to the question)

= Cost of 5 kg of wheat is 30.50 rupees

Cost of 1 kg of wheat is,

= 30.50/5

= 61 rupees

Now, (a) What will be the cost of 8 kg of wheat?

Cost of 8 kg wheat

= (8 × 6.1)

= 48.8 rupees

(b) What quantity of wheat can be purchased in ₹ 61?

= The quantity of wheat purchased in 61 rupees

= 61//6.1

= 10 kg

Question no – (9)

Solution :

The cost of 60 envelopes is Rs 90 …(according to the question)

Cost of 60 envelopes is 90 rupees

Cost of 1 envelopes is,

= 90/60

= 1.5 rupees

(a) Find the cost of 10 envelopes.

= Cost of 10 envelopes

= (10 × 1.5)

= 15 Rupees.

(b) How many envelopes can be purchased for Rs 30?

= The number of envelopes in 30 rupees,

= 30/1.5

= 20

Question no – (10)

Solution :

As per the question,

Cost of 12 oranges is 30 rupees.

Cost of 1 oranges is,

= 30/12

= 5/3 rupees

Cost of 15 oranges is,

= 5/3 × 15

= 25 rupees

Question no – (11)

Solution :

Ankita purchases 10 notebooks for 120 rupees,

Ankita purchases 1 notebooks for,

= 120/10

= 12 rupees

Garima buys 8 notebooks for 104 rupees,

Garima buys 1 notebook for,

= 104/8

= 13 rupees

Therefore, Ankit got the notebooks at a cheaper rate.

Question no – (13)

Solution :

Anish made 42 runs in 6 over,

Anish made,

= 42/6

= 7 runs in 1 over.

Anup made 63 runs in 7 over,

Anup made,

= 63/7

= 9 runs 1 over

Therefore, Anup made more runs per over.

Ratio and Proportion Chapter Check-up Solution

Question no – (1)

Solution :

(a) 5 minutes to 40 seconds

= (5 × 60) : 40

= 300 : 40

= 15 : 2

(b) 700 m to 12 km

= 700 : (12 × 1000)

= 700 : 12000

= 7 : 120

(c) a dozen to a score

= 12 : ?

(d) 7 days to 4 weeks

= 7 : (4 × 7)

= 1 : 4

Question no – (2)

Solution :

(a) 15 : 175 in simplest form,

= 3: 35

(b) 65 : 91 in simplest form,

= 5 : 7

(c) 90 : 279 in simplest form,

= 10 : 31

Question no – (3)

Solution :

(a) 2/3, 4/6

= 2/3 = 4/6

Because, 2/3 is the simplest form of 4/6

(b) 8/4, 2/1

= Because 2/1 is the simplest form of 8/4

(c) 4/5, 12/20

= 4/5 ≠ 12/20

Question no – (5)

Solution :

As per the question we know,

A line segment 56 cm long is to be divided into two parts in the ratio of 2 : 5.

Now, Length of the first part,

= 56 × 2/7

= 16 cm

Length of the second part,

= 56 × 5/7

= 40 cm

Thus, the length of each part will be 16 cm and 40 cm respectively.

Question no – (6)

Solution :

According to the question,

An alloy contains only zinc and copper and they are in the ratio of 7 : 9.

= Zink : Copper

= 7 : 9

In 8 kg alloy, amount of copper is,

= 8 × 9/16

= 9/2

= 4.5 kg

Hence, the weight of copper in the alloy will be 4.5 kg.

Question no – (7)

Solution :

According to the question,

Bachhu Manjhi earns 24000 in 8 months

Bachhu Manjhi earns,

= 24000/8

= 3000 in 1 month

(a) how much does he earn in one year?

So, Bachhu Majni earns,

= (3000 × 12)

= 36000 in one year

(b) in how many months does he earn 42000?

= He hears 42000

= in 42000/3000

= 14 months.

Question no – (8)

Solution :

(a) 12 : 6 : : 18 : x

= x = 6 × 18/12

= x = 9

So, the value of x is 9

(b) 5 : 3 : : 25 : x

= x = 3 × 25/5

= x = 15

Hence, the value of x is 15

(c) 20 : 30 : : 60 : x

= x = 30 × 60/20

= x = 90

Thus, the value of x is 90

(d) 4 : 60 : : 3 : x

= x = 60 × 3/4

= x = 45

Therefore, the value of x is 45

Question no – (9)

Solution :

40/25 is greater than 1 other ratios are smaller than 1

Therefore, 40/25 is the greatest.

Question no – (10)

Solution :

As per the given question,

Mathematics textbook for Class VI has 320 pages.

The chapter ‘symmetry’ runs from page 261 to page 272.

Now, {(272 – 261) + 1} : 320

= 12 : 320

= 3 : 80

Thus, the ratio of the number of pages of this chapter to the total number of pages of the book is 3 : 80

Question no – (11)

Solution :

From the question we get,

In a box, the ratio of red marbles to blue marbles is 7 : 4.

Since, (7 + 4) = 11

And only 22 is divisible by 11

That way, 22 is the total number of marbles.

Question no – (12)

Solution :

According to the question,

On a shelf, books with green cover and that with brown cover are in the ratio 2 : 3.

If there are 18 books with green cover,

Therefore,

= 2 : 3 : : 18 : x

2 × x = 3 × 18

or, x = 3 × 18/2

= x = 27

Thus, the number of books with brown cover is 27 books.

Question no – (13)

Solution :

(a) 3/5 = __/20

= 3/5 = 15/20

(b) __/18 = 2/9

= 4/18 = 2/9

(c) 8/__ = 32/4

= 8/10 = 32/4

(d) __/45 = 16/40 = 24/__

= 27/45 = 16/40 = 24/60

(e) 16/36 = __/63 = 36/__ = __/117

= 16/36 = 28/63 = 36/81 = 52/117

Question no – (15)

Solution :

According to the question,

Two numbers whose sum is 100 and whose ratio is 9 : 16.

The numbers are,

= (100 × 9/(9 + 16) and (100 × 16/(9 + 16)

= (100 × 9/25) and (100 × 16/25)

= 36 and 64

Thus, the required numbers are 36 and 64.

Question no – (16)

Solution :

Given in the question,

The yield of wheat from 8 hectares of land is 360 quintals.

Let x hectares land is required

8 : 360 : : x : 540

x = 540 × 8/360

= x = 12 hectares

Therefore, 12 hectares of land required for a yield of 540 quintals.

Question no – (17)

Solution :

Given in the question,

The quarterly school fee in a school for Class VI is 540.

Now, Fees for 3 months is 540 rupees

Fees for 1 month is 540/3 = 180 rupees

Fees for 7 months is,

= (180 × 7)

= 1260 rupees

Hence, the fee for seven months will be 1260 rupees.

Question no – (18)

Solution :

In the question we get,

Cost of 2 kg apple is 280 rupees

Cost of 1 kg apple is,

= 280 ÷ 2

= 140 rupees

Now, (a) Cost of 7 kg apple is,

= (140 × 7)

= 980 rupees

(b) In 700 rupees,

= 700/140

= 5 kg apple can be bought

Question no – (19)

Solution :

According to the question,

The number of milk teeth in human beings is = 20

the number of permanent teeth is = 32.

So, the ratio is,

= 20 : 32

= 5 : 8

Thus, the ratio of the number of milk teeth to the number of permanent teeth is 5 : 8

Question no – (20)

Solution :

(a) Africa to Europe?

= 26 : 10

= 13 : 5

(b) Australia to Asia?

= 8 : 44

= 2 : 11

(c) Antarctica to Combined area of North America and South America?

= 13 : (17 + 18)

= 13 : 35

Question no – (21)

Solution :

Earth rotates 3600 in 24 hours …(according to the question)

Earth rotates 360/24 = 150 in 1 hours

Earth rotates (15 × 2)0 = 300 in 2 hours

Question no – (22)

Solution :

For 15 days, Shivangi needs (15 × 2) = 30 tablets

Let the cost of 30 tablets be x rupees.

10 : 17 :: 30 : x

10x = 17 × 30

x = 17 × 30/10

= x = 51 rupees

Thus, she required 51 rupees to pay for her medical bill for 15 days.

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Updated: June 6, 2023 — 6:18 am