Question

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces
1) I becomes
if we only add I to the denominator. What is the fraction?
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as
de Sona. How old are Nuri and Sonu?
The son of the digits of a two-digit number is 9. Also, nine times this number is
the number obtained by reversing the order of the digits. Find the number.
Meena went to a bank to withdraw 7 2000. She asked the cashier to give lier
10 and 1100 notes only. Meena got 25 notes in all. Find how many notes of
50 and 100 she recerved.​

Answer 1

$\huge\underline\green{ Correct \:Question}$

1. If we add 1 to numerator, and subtract 1 from the denominator, a fraction reduce to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?

2. 5 years ago Nuri was thrice as old as Sonu. 10 years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu ?

3. The sum of the digits of a two digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

4. Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.

$\huge\underline\pink{Explanation :}$

$\large\underline\bold\blue{Part 1 :}$

1. Let, us take a fraction

➣$\frac{2}{5} = 0.4$

Adding, 1 to the denominator it becomes

➣$\frac{2}{6} = 0.33$

So, the fraction decreases.

【Note : If the denominator increases the fraction decreases and if the denominator decreases the fraction increases.】

$\large\underline\bold\blue{Part 2 :}$

2. Let, Sonu's present age be x

5 years ago Sonu's age = (x - 5)

5 years ago Nuri' age = 3(x - 5)

Nuri's present age = 3(x - 5) + 5

10 years later Sonu's age = (x + 10)

10 years later Nuri's age = 2(x + 10)

Nuri's present age = 2(x + 10) - 10

According to Sum,

➣3(x - 5) + 5 = 2(x + 10) - 10

➣3x - 15 + 5 = 2x + 20 - 10

➣3x - 10 = 2x + 10

➣3x - 2x = 10 + 10

➣x = 20

Sonu's present age

= 20 years

Nuri's present age

= 3(x - 5) + 5

= 3(20 - 5) + 5

= 3(15) + 5

= 45 + 5

= 50 years

$\large\underline\bold\blue{Part 3}$

Let, digit in one's place be x.

So, the ten's digit will be (9 - x)

Number

= 10 × ( ten's digit ) + one's digit

= 10 × ( 9 - x ) + x

= 90 - 10x + x

= 90 - 9x

Number reversed

= 10 × ( ten's digit ) + one's digit

= 10 × ( x ) + ( 9 - x )

= 10x + 9 - x

= 9x + 9

According to sum,

9 times the number = 2 the number reversed

➣9 ( 90 - 9x ) = 2 ( 9x + 9)

➣810 - 81x = 18x + 18

➣810 - 18 = 18x + 81x

➣792 = 99x

➣99x = 792

➣x = 8

Ten's digit

= 9 - x

= 9 - 8

= 1

Number

= 10 × ( ten's digit ) + one's digit

= 10 × 1 + 8

= 10 + 8

= 18

$\large\underline\bold\blue{Part 4 }$

Let, the number of notes of ₹50 be x and ₹100 notes be y.

x + y = 25

x = 25 - y

According to sum,

➣50x + 100y = 2000

➣50 ( x + 2y ) = 2000

➣( x + 2y ) = 40

➣( 25 - y + 2y ) = 40 [ Substituting x with ( 25 - y )]

➣25 + y = 40

➣y = 15

No. of 100 notes = 15

No. of 50 notes = 25 - 15 = 10