Latest TCS Aptitude Question SOLUTION: When we multiply a two digit number by sum of its digits 144 is achieved. If we reverse the number and multiply it by sum of digits,we get 252. What is the last digit of original n

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When we multiply a two digit number by sum of its digits 144 is achieved. If we reverse the number and multiply it by sum of digits,we get 252. What is the last digit of original number ?

Asked In TCS charles (9 years ago)

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akhil achuthan  (9 years ago)

let the number as 10x+y where x is the digit of unit place and y is other digit.
Given (10x+y)(x+y)=144
10x^2+2xy+y^2=144 eq 1
and (10y+x)(x+y)=252
10y^2+2xy+x^2=252 eq 2
eq2 - eq1 = 9y^2-9x^2=108
=> y^2-x^2=12.
if y=4 & x=2 then number will be 24 which satisfies all given conditions.
ans. 24.

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Pratik Chaturlal Chaudhari  (9 years ago)

Last digit is 4
24*6=144;
42*6=252.

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jyotsna  (9 years ago)

xy(10x+y)=144
yx(10y+x)=252
From this 2 equations we get y=2x.substuting in any one of the eqaution we get x=cube root of (6).by substuting value of x.we get y =2*cuberoot of(6).so we get value as 3.6342=4

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amit jain  (9 years ago)

24*6=144 so original no.is 24 n ans is 4

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Rohit Kumar  (9 years ago)

answer is 4.
The original number is 24. Best way to find answer is going through options.

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gaurav rai  (9 years ago)

24*(2+4)=144 and its reverse 42*(4+2)=251...so ans is 4...by raj gautam

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logeswaran  (9 years ago)

24 is the number 24*6=144
reverse 42*6=252
last digit of original number is 4

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RITESH KUMAR  (9 years ago)

ans is 4
because we get the expression y^2-x^2=12 and only x=2 and y=4 is satisfying this equation.

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aman sharma  (9 years ago)

trick 144 then last digit must be 4 and when we get again 4 when multiplied by 6 so 10th place is 6-4 =2

same for 252 last digit of number is also 2 and when we get last digit 2 in 2s table 6 so first digit is 6-2 =4

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