Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

A two-digit number is such that the product of its digits is 15. If 18 is added to the number, the digits interchange their places. Find the number.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

It is given that a two-digit number is such that the product of its digits is 15.
It is also given that if 18 is added to the number, the digits interchange their places.
Let the digits of the number at tens place

x

and at unit place be

y

.
Therefore, the given number is

10 x + y

.
As the product of the digits of the number is 15,

⇒ x y = 15 ⇒ y = 15 x ... (1)

If 18 is Added to the number. The digits interchange their places.

⇒ 10 x + y + 18) = 10 y + x ⇒ 9 x − 9 y = − 18 ⇒ x − y = − 2... (2)

Substituting (1) in equation (2) to determine the value of

x

⇒ x − y = − 2 ⇒ x − 15 x = − 2 ⇒ x 2 + 2 x − 15 = 0 ⇒ x 2 + 5 x − 3 x − 15 = 0 ⇒ x (x + 5) − 3 (x + 5) = 0 ⇒ (x − 3) (x + 5) = 0

Solving these factors by equating both the terms to 0,

⇒ x − 3 = 0 ⇒ x = 3

And,

⇒ x + 5 = 0 ⇒ x = − 5

Therefore,

x = 3, − 5

.
Since the digits are not negative,

x = 3

.
Substitution 3 for

x

in equation (1) to determine the value of

y

⇒ y = 15 x ⇒ y = 153 ⇒ y = 5

Then the number is,

= 10 x + y = 10 (3) + 5 = 35

The number is 35.
Hence, the correct option is 3.

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET