Question

A two digit number is represented as "IJ". If the value of J2 – I2 is equal to ten times the value of J-I, the two digit number is
(A) 26
(B) 84
(C) 48
(D) 37

Answer 1

Question:-

A two digit number is represented as "IJ". If the value of J² – I² is equal to ten times the value of J-I, the two digit number is

(A) 26

(B) 84

(C) 48

(D) 37

Answer:-

Option D) 37

$\rule{100}2$

Solution:-

Two digit number is represented as IJ.

From above line it's clear that I is ten's digit number and J is one's digit number.

We can represent it as = I × 10 + J

→ I0 + J

→ IJ

Now, according to question

→ J² - I² = 10(J - I)

Option A) 26. Here, ten's digit number = 2 and one's digit number = 6.

So, I = 2 and J = 6

→ (6)² - (2)² = 10(6 - 2)

→ 36 - 4 = 10(4)

→ 32 = 40

LHS ≠ RHS

Option B) 84

→ (4)² - (8)² = 10(4 - 8)

→ 16 - 64 = 10(-4)

→ - 48 = - 40

LHS ≠ RHS

Option C) 48

→ (8)² - (4)² = 10(8 - 4)

→ 64 - 16 = 10(4)

→ 48 = 40

LHS ≠ RHS

Option D) 37

→ (7)² - (3)² = 10(7 - 3)

→ 49 - 9 = 10(4)

→ 40 = 40

LHS = RHS

•°• Two digit number is 37.

(Where ten's digit number i.e. I is 3 and one'digit number i.e. J is 7)

Answer 2

Question :----

• A two digit number is represented as "IJ". If the value of J² – I² is equal to ten times the value of J-I, the two digit number is ?

My Approach :----

it has been say that the Two digit number is IJ .

So,

→ Number at unit digit = J

→ Number at Ten's digit = I .

Or, we can say that, our Number is = (10I + J)

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According to Question Now,

→ J² - I² = 10(J - I)

[ since, (a²-b²) is Equal to (a+b)(a-b) ]

→ (J+I)(J-I) = 10(J-I)

[ Cancel (J-I) both sides we get ]

→ J + I = 10

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Now, Given above data , we cant Find two number whose sum is 10, so, Lets take Our Options Now,

Option (1) ,

→ 2 + 6 = 8 = Not Equal to 10.

Option (2)

→ 8+4 = 12 = Not Equal to 10.

Option (3)

→ 4+8 = 12 = Not Equal to 10.

Option (4)

→ 3+7 = 10 = (J+I)

so, this is our correct answer (D) 37...

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Verification :--

our Two digit Number represented as IJ = 37

→ I = 3

→ J = 7 .

Now, Given ,

→ J² - I² = 10(J - I)

putting values we get,

→ (7)² - (3)² = 10(7-3)

→ 49 - 9 = 10*4

→ 40 = 40

Hence, Proved our Required Number is Correct .

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