# Fractions

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.

1. A man spends one-fifth of his salary for household expenditures and one fourth of the remaining for his children. He donates one-third of what is left to charity and saves the rest. If he saves Rs.20000, find his salary.

A. Rs.100,000

B. Rs.50000

C. Rs.80,000

D. Rs.60,000

Ans: Option B

Explanation:

Let his salary be Rs.x

Amount spent for household expenditures = x/5

Amount spent for children =(1/4)*(4x/5) = x/5

Amount left = x-(2x/5) = 3x/5

Amount donated to charity = (1/3)*(3x/5) = x/5

Amount left =Amount saved

x-(3x/5) = 20000

2x/5 = 20000

x=Rs.50000

2. By how much is one-third of 570 lesser than half of 450?

A. 60

B. 45

C. 30

D. 35

Ans: Option D

Explanation:

(1/3)*570 = 190

(1/2)*450 = 225

Then, 225-190=35

3. 60% of a class is boys and 40% are girls. 30% of the girls and 50% of the boys went for a trip. What fraction of the class didn't go for the trip?

A. 29/50

B. 21/50

C. 31/50

D. 19/50

Ans: Option A

Explanation:

Let the no. of students in the class be x.

No. of students who went for the trip

= 30% of 0.4x + 50% of 0.6x

=> 0.12x+0.3x

=> 0.42x 0.58x

Students did not go for the trip. 0.58x/x => 58/100

=> 29/50

4. Shyam spends one-fifth of his salary for his children's education, 20% for household expenditures, 10% for other miscellaneous expenses and saves the rest. What fraction of his salary does he save?

A. 1/2

B. 2/5

C. 1/4

D. 3/5

Ans: Option A

Explanation:

No explanation

5. A box contains 140 ice-creams, 30% of which are strawberry, two-sevenths are chocolate, 5% are mango and the rest are vanilla. How many ice-creams are vanilla flavoured?

A. 14

B. 49

C. 35

D. 51

Ans: Option D

Explanation:

No. of strawberry ice-creams = 30% of 140 = 42

No. of chocolate ice-creams = (2/7)*140 = 40

No. of mango ice-creams = 5% of 140 = 7

No. of vanilla = 140-(42+40+7) = 51

6. If x=1/y and y=1/z, then

A. x=1/z

B. x=1/z²

C. x=z

D. None of the above

Ans: Option C

Explanation:

x=1/y

x=1/(1/z)

= z

7. If a=(3/7), b=(3/7)2; and c=?(3/7), then which of the following is true?

A. b<a<c

B. b<c<a

C. c<a<b

D. a<c<b

Ans: Option A

Explanation:

Squaring a proper fraction will make it smaller.

=> (3/7)² = 9/49

Compare 3/7 and 9/49

3/7 = 21/49

9/49<21/49

(3/7)²<3/7<?(3/7) b<a<c

8. The sum of a number and its reciprocal is 17/4. Find the number.

A. 8

B. 6

C. 10

D. 4

Ans: Option D

Explanation:

Let the number is x

x+(1/x) = 17/4

(x²+1)/x = 17/4

Substitute the options in the above equations. x=4

9. If x=5 and y=7, find the value of (x2-14x+49)/(25-10y+y2 )

A. 1

B. 2

C. 3

D. 4

Ans: Option A

Explanation:

(x²-14x+49)

= (x-7)²

= (5-7)²

= 4

Then, (25-10y+y²)

= (5-y)²

= (5-7)²

= 4

Hence,   (x2-14x+49)/(25-10y+y2 ) = 4/4 = 1

10. Find the decimal value of 30% of 20% of (7/12).

A. 0.7

B. 0.07

C. 0.035

D. 0.35

Ans: Option C

Explanation:

(30/100)*(20/100)*(7/12) = 7/200 = 0.035

11. If x=2 and y=3, find the value of x+(1/x)+(1/y)+y

A. 35/6

B. 6

C. 5/2

D. 7/2

Ans: Option A

Explanation:

x+(1/x)+(1/y)+y

= 2+(1/2)+3+(1/3)

= 35/6

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