The sum of the digits of a two 1 point
digits number is 12. The number
obtained by interchanging the
two digits exceeds the given
number by 18. Find the number.
Answers
Step-by-step explanation:
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NCERT Exemplar Class 10 Maths Chapter 5 Arithmetic Progressions
June 28, 2019 by Bhagya
NCERT Exemplar Class 10 Maths Chapter 5 Arithmetic Progressions
NCERT Exemplar Class 10 Maths Chapter 5 Exercise 5.1
Choose the correct answers from the given four options:
Question 1.
In an AP, if d = -4, n = 7, an = 4, then a is equal to
(A) 6
(B) 7
(C) 20
(D) 28
Solution:
(D)
In an AP,
an = a + (n – 1 )d
⇒ 4 = a + (7 – 1) (-4) [by given conditions]
⇒ 4 = a + 6(-4) ⇒ 4 + 24 = a
∴ a = 28
Question 2.
In an AP, if a = 3.5, d = 0,n = 101, then an will be
(A) 0
(B) 3.5
(C) 103.5
(D) 104.5
Solution:
(B)
In an AP,
an = a + (n – 1)d = 3.5 + (101 – 1) × 0
[by given conditions]
∴. an =
Given :-
- The sum of the two digits number is 12. The number obtained by interchanging the two digits exceeds the given number by 18
To find :-
- Required numbers
Solution :-
Let the tens digit be x then ones digit be y
- Original number = 10x + y
Sum of the two digits number is 12.
- x + y = 12 ----(i)
The number obtained by interchanging the two digits exceeds the given number by 18
- Reversed number = 10y + x
→ 10x + y + 18 = 10y + x
→ 10x - x + y - 10y = - 18
→ 9x - 9y = -18
→ 9(x - y) = - 18
→ x - y = - 2 ----(ii)
Add both the equations
→ x + y + x - y = 12 - 2
→ 2x = 10
→ x = 10/2
→ x = 5
Put the value of x in equation (i)
→ x + y = 12
→ 5 + y = 12
→ y = 12 - 5
→ y = 7
Hence,
- Tens digit = x = 5
- Ones digit = y = 7
Therefore,
- Original number = 10x + y = 57
- Reversed number = 10y + x = 75