Question

10. A fraction is such that the numerator is five less than
the denominator. Also four times the numerator is one
more than the denominator. Find the fraction.
(A) 4/9 (B) 3/8
(C) 2/7
(D) 7/12​

Answer 1

ANSWER :-

• Fraction is 2/7 (Option C)

GIVEN :-

• Numerator is five less than denominator.

• For times the numerator is one more than the denominator.

TO FIND :-

• The fraction.

APPROACH :-

• We will make equation with the help of given data .Then we can find out the numerator and denominator .

Fraction is [numerator/denominator].

SOLUTION :-

We know , numerator is five less than denominator.

So, let the numerator be 'x' .

Numerator is 5 less than denominator.

Denominator will be 'x+5'.

Also , Four times the numerator is one more than denominator.

➛ 4(x) = 1 + (x+5)

Solving furthur ,

➛ 4x = 1 + x + 5

➛ 4x = 6 + x

➛ 4x - x = 6

➛ 3x = 6

➛ x = 2

Now we will substitute the value of "x" in the assumed values of numerator and denominator.

♦ Numerator → x = 2

♦ Denominator → (x+5)

ㅤㅤㅤㅤㅤㅤㅤ = 2+5

ㅤㅤㅤㅤㅤ ㅤㅤ= 7

Hence , numerator is 2 and denominator is 7.

Fraction becomes 2/7. (Option C)

Answer 2

Required Answer :

Given -

• A fraction is such that the numerator is five less than the denominator.

• Also four times the numerator is one

more than the denominator.

To Find -

• The Fraction

Solution -

To find the Fraction, we will one by one take all the fractions given to us, which are 4/9, 3/8, 2/7 and 7/12, and then with the help of the clues we will check which fraction matches the clues, so let's do it!

(A) 4/9 :

• A fraction with numerator five less than the denominator ( 9 - 4 = 5 ) ✔

• Also four times the numerator is one

more than the denominator ( 4 × 4 = 16 which is not 1 more than 9 ) ❌

(B) 3/8

• A fraction with numerator five less than the denominator ( 8 - 3 = 5 ) ✔

• Also four times the numerator is one

more than the denominator ( 3 × 4 = 12 which is not 1 more than 8 ) ❌

(C) 2/7

• A fraction with numerator five less than the denominator ( 7 - 2 = 5 ) ✔

• Also four times the numerator is one

more than the denominator ( 2 × 4 = 8 which is 1 more than 7 ) ✔

(D) 7/12

• A fraction with numerator five less than the denominator ( 12 $-$ 7 = 5 ) ✔

• Also four times the numerator is one more than the denominator ( 7 × 4 = 28 which is not 1 more than 12 ) ❌

So, clearly 2/7 is the fraction and the required option is (C)

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