A number consists of two digits. Six times the tens digit is equal to twice the units digit. If the digits are reversed, twice the new number is 10 more than four times the original number. Find the number.

Question

apoorvk · Answer

let one's digit be x and ten's place digit be y. so the no. is 10y+x
the 6y=2x ...(i)
reversing the digits the no. will become 10x+y

so 2(10x+y)=4(10y+x).... (ii)


simplify, solve (i) and (ii), find x and y, and enjoy!!

myininaya · Answer

So we have a two digit number 
Lets call it $$d_1d_2 \text{ where } d_1d_2=10 \cdot d_1 +1 \cdot d_2 \text{ since } d_1 \text{ is the ten's digit and } d_2 \text{ is the one's digit}$$
$$6 \cdot d_1= \cdot 2d_2  \text{ said 6 times the tens digit is equal to twice the units digit}$$
$$d_2d_1 \text{ digits reversed}$$
This means we now have
$$d_2d_1=10 \cdot d_2+1 \cdot d_1 \text{ since } d_2 \text{ is the 10's digit and } d_1 \text{is the one's digit}$$
So we have:
$$2(d_2d_1)=10+4 \cdot (d_1d2)$$ $$\text{ since it said the new number is 10 more than 4 times the original number}$$

apoorvk · Answer

oopss!! sorry forgot to add 10 in the RHS of equation (ii)!!! will read now:

2(10x+y)=4(10y+x) +10 ..(ii)

myininaya · Answer

$$2(10d_2+d_1)=10+4(10d_1+d_2)$$
Since $$d_2d_1=10d_2+d_1 \text{ and } d_1d_2=10d_1+d_2$$

myininaya · Answer

oh and it looks like apoorvk got it
go you! lol