The some of the digits of a three digit number is
20. The middle digit is equal to one-fourth The
some of the other 2. If the order of the digit
to be reversed, the number increases by 198
find the original
number.
Answers
I hope this method will help you.
Concept: Linear Equations in two variables.
Solution :-
Let us assume that, the original three digit number is 100x + 10y + z .
So,
→ New number after digits are reversed = 100z + 10y + x .
A/q,
→ (100z + 10y + x) - (100x + 10y + z) = 198
→ 100z - z + 10y - 10y + x - 100x = 198
→ 99z - 99x = 198
→ 99(z - x) = 198
→ (z - x) = 2 ----------- Eqn.(1)
also,
→ x + y + z = 20 ------- Eqn.(2)
and,
→ y = (1/4)(x + z)
→ 4y = x + z ------------ Eqn.(3)
putting value of Eqn.(3) in Eqn.(2),
→ (x + z) + y = 20
→ 4y + y = 20
→ 5y = 20
→ y = 4
putting value of y in Eqn.(3) now,
→ x + z = 4 * 4
→ x + z = 16 --------- Eqn.(4)
adding Eqn.(4) and Eqn.(1) now,
→ (x + z) + (z - x) = 16 + 2
→ x - x + z + z = 18
→ 2z = 18
→ z = 9
putting value of z in Eqn.(1) now,
→ 9 - x = 2
→ x = 9 - 2
→ x = 7
therefore,
→ Original number = 100x + 10y + z = 100 * 7 + 10 * 4 + z = 700 + 40 + 9 = 749 (Ans.)
Hence, Original number is equal to 749 .
Verification :-
→ 9 + 4 + 7 = 20
→ 947 - 749 = 198
→ 4 * 4 = 9 + 7
Learn more :-
Consider the sequence defined by ak=1/k2-k for k ≥ 1. Given that aM + aM + 1 + …………+ aN – 1=1/29 for positive integers M...
https://brainly.in/question/42384271
(c)
75. From a number M subtract 1. Take the reciprocal of
the result to get the value of 'N'. Then which of the
followi...
https://brainly.in/question/39499253