Question

a two digit number is 4 times the sum and 3 times the product of its digit .Find the number

Answer 1

Answer: required no. can be 0 and 24

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Step-by-step explanation:

Let no. = 10x + y

Given-

10x + y = 4(x+y)

10x + y = 4x + 4y

6x - 3y = 0

2x - y = 0

y=2x(i)

Also, 10x + y = 3xy

Placing (i) in above-

12x = 6x^2

12x-6x^2=0

(6x)(2-x)=0

x=0/6=0 and x=2

Clearly required no. can be 0 and 24

Answer 2

Suppose unit digit be p

Tens digit be m

Number = 10m + p

Now

10m + p = 4(p + m)

6m - 3p = 0

2m - p = 0 .......... (1)

Also

10m + p = 3pm

10m + 2m = 3pm ..... (From equation 1)

12m = 3pm

3m (4 - p) = 0

m = 0

p = 4

Avoid 0

p = 4

From equation 1 we get :-

2m - 4 = 0

2m = 4

${\implies m = \dfrac{4}{2}}$

Required Number :-

= 2 × 10 + 4

= 24

Q.E.D