Ex 3.3 Q2 (iii) - The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Solution:-Let,
Unit's digit no. = x
Ten's digit no. = y
∴ Original Number = 10y + x
∴ Number obtained after reversing the
order of digits = 10x + y
➙ Given that, the sum of the digits of the number is 9,
∴ x + y = 9
∴ x = 9 - y ------- ( 1 )
➙ Also, nine times of the number is twice the number obtained by reversing the order of the digits,
∴ 9(10y + x) = 2(10x + y)
∴ 90y + 9x = 20x + 2y
∴ 90y - 2y = 20x - 9x
∴ 88y = 11x
*Taking 11 as common
∴ 8y = x
∴ x = 8y ------- ( 2 )
*Putting x = 9 - y in Eqⁿ( 2 )
∴ 8y = 9 - y
∴ 8y + y = 9
∴ 9y = 9
∴ y =
9
/
9
∴ y = 1
➙ Putting y = 1 in Eqⁿ( 1 )
∴ x = 9 - 1
∴ x = 8
Therefore,
*Unit's digit no. = x = 8
*Ten's digit no. = y = 1
∴ Original Number
= 10y + x
= 10(1) + 8
= 10 + 8
= 18
Hence,
The required number is 18.
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Try This..
✒ A two-digit number is such that the product of its digits is 18. If 63 is subtracted from the number, the digits interchange their places. Find the number.
✒ A number consists of two digits whose sum is 5. If 9 is added to the number, its digits are reversed. Find the number.
✒ The sum of the digits of a two-digit number is 7. If the digits are reversed, the number increases by 27. What is the number?
❌ Common Mistakes
Confusing the number with its digits:▸ Remember, 10x + y is the number, not just x and y.Reversing incorrectly:▸ The reversed number is 10y + x, not the other way around.Missing equation simplification:▸ Simplify the second equation carefully to avoid calculation errors.
📝 Related Questions:-
- Ex 3.3 Q2 (i) - If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?
- Ex 3.3 Q2 (ii) - Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
- Ex 3.3 Q2 (iv) - Meena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and ₹100 she received.
- Ex 3.3 Q2 (v) - A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Queries Solved:-
Class 10 Ex 3.3
Ex 3.3 Q2 iii Class 10
Class 10 Ex 3.3 Q2 iii
Class 10 Chap 3 Ex 3.3 Q2 iii
Class 10 Pair Of Linear Equations in Two Variables
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