Question

The fraction obtained by dividing a two digit
number by the number obtained by reversing
the digits is 8/3. The sum of the number is 9. Find the original number.​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a number which when divided by the number obtained by reversing its digit gives a fraction 8/3
• Sum of digits of number is 9

To Find:

• We have to find the original number

Solution:

Let Tens digit of number = x

Unit digit of number = y

$\boxed{\sf{Original \: Number = 10x + y}}$

Given that sum of digit is 9

$\implies \sf{x + y = 9}$

$\implies \boxed{\sf{y = 9 - x }}$ ---------- 1

_______________________________

$\underline{\large\mathfrak\red{According \: to \: the \: Question:}}$

The fraction obtained by dividing a two digit number by the number obtained by reversing the digits is 8/3

$\implies \boxed{\bold{\dfrac{\text{Original \: Number}}{\text{Reversed \: Number }} = \dfrac{8}{3}}}$

$\implies \sf{\dfrac{10x + y}{10y+x} = \dfrac{8}{3} }$

Cross Multiplying the Terms

$\implies \sf{3 \: ( 10x + y ) = 8 \: ( 10y + x ) }$

$\implies \sf{30x + 3y = 80y + 8x}$

$\implies \sf{30x - 8x = 80y - 3y}$

$\implies \sf{22x = 77y}$

$\implies \sf{2x = 7y}$

Substituting the values of y from Equation 1

$\implies \sf{2x = 7 \: ( 9 - x ) }$

$\implies \sf{2x = 63 - 7x}$

$\implies \sf{9x = 63 }$

$\implies \sf{x = \dfrac{63}{9}}$

$\implies \boxed{\sf{x = 7}}$

_______________________________

Putting x = 7 in Equation 1 , we get

$\implies \sf{y = 9 - 7}$

$\implies \boxed{\sf{y = 2}}$

Original number is as follows :

$\implies \sf{10 \: (7) + 2}$

$\implies \sf{70 + 2}$

$\implies \sf{72 }$

________________________________

$\huge\underline{\sf{\red{A}\orange{n}\green{s} \pink{w} \blue{e}\purple{r}} }$

$\large\boxed{\sf{Original \: Number = 72}}$

________________________________

$\huge\mathtt\green{Verification:}$

☞ The fraction obtained by dividing a two digit number by the number obtained by reversing the digits is 8/3

$\sf{Fraction = \dfrac{72}{27}}$

$\sf{Fraction = \dfrac{8}{3}}$

$\large\red{\underline{\underline{\sf{Hence \: Verified \: !!! }}}}$

Answer 2

Explanation:

Required Answer:-

A – 405, Vijay Laxmi Apartments, Lajpat Nagar, Delhi

Date - 18 - 2 - 2021

ABC address (receiver's address)

Dear Abhinav

Hope you are in good health and spirit, I am also fine here. Today, I want to tell you an interesting thing. An international Book fair is going to take place in my city on 23 February in pragati maidan, Delhi, and it's said to be a very big and amazing book fair. I also wished to visit that book fair once in my life, but I don't want to go alone, so, I am inviting you to come to Delhi and stay with me for few days and visit to that book fair with me, as you also loves books a lot. We can also buy any book from there, it's going to be an amazing and memorable experience for both of us, so please I request you that you should come here and we both will go to that fair together. I will be waiting for your reply, take care of you and your family.

Your lovingly

Nikita

Learn more !!

What is a letter?

⟶ A letter is a form of written communication which is given to another person telling, asking or complaining about any purpose.

⟶ Letter was widely used in olden times of India. It took them few days to reach another address.

2 types of letters :-

1] Formal letter :-

Formal letters are written to any official people, like police, principal, teacher, governor, mayor, etc.

→ We use Formal language in this, and use formal greeting like respected/sincerely,etc.

2] Informal letter :-

→ Informal letters are written to your near and dear ones for eg; Uncle,aunt, brother, sister.

→ Language is always formal, like dear, etc.

Format of letter -

1. Formal letter -

Sender's address

---

Date

---

Reciever's address

---

Subject

---

Salutation (Respected sir/ma'am)

Content

---

Salutation 2 (Your sincerely)

Your name

Informal letter -

Sender's address

---

Date

---

Reciever's address

---

Subject

---

Salutation (Dear.)

Body

---

Salutation 2 (your lovingly)

Your name