Math, asked by mahipatil1979, 4 months ago

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

Answered by AmishaUS5105
0

I hope this method will help you.

Concept: Linear Equations in two variables.

Attachments:
Answered by RvChaudharY50
0

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

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