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- Question
- A, B, C and D purchase a gift worth ? 60. A pays 1/2 of what others are paying, B pays 1/3rd of what other are paying and C pays 1/4th of what others are paying. What is the amount paid by D?
Options- A. 14
- B. 15
- C. 16
- D. 13
- Correct Answer
- 13
ExplanationLet A, B, C and D pay ?x, ?y, ?z and ?a
According to the question,
x = 1/2(y + z + a)
2x = (y + z + a) ..........(i)
y = 1/3(x + z + a)
3y = (x + z + a) ...........(ii)
z = 1/4(x + y + a)
4z = (x + y + a) ..........(iii)
Also, x + y + z + a = 60 ...............(iv)
Now, put the value of x + y + a = 4z from (iii) in (iv)
Then, 4z + z = 60 ? 5z = 60
? z = 12
Similarly, on putting the value of x + z + a = 3y from (ii) in (iv), we get
3y + y = 60 = ? 4y = 60
? y = 15
Again, on putting the value of (y + z + a) = 2x from (i) in (iv), we get
2x + x = 60 ? 3x = 60
&ther4; x = 20
Now, x + y + z + a = 60
On putting the value of x, y and z, we get
12 + 15 + 20 + a = 60
? a = 60 - 47 = ? 13 - 1. If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 150%, the resultant fraction is 9/35. What is the original fraction?
Options- A. 3/10
- B. 2/15
- C. 3/16
- D. 2/7 Discuss
- 2. A man reads 3/8 of a book on a day and 4/5 of the remainder on the second day. If the number of pages still unread are 40, then how many pages did the book contain?
Options- A. 300
- B. 500
- C. 320
- D. 350 Discuss
- 3. 1/8 part of a pencil is black and 1/2 part of the remaining is white. If the remaining part is blue and length of this blue part is 31/2 cm, then find the length of the pencil.
Options- A. 6 cm
- B. 7 cm
- C. 8 cm
- D. 9 cm Discuss
- 4. In the year 2011, Shantanu gets ? 3832.5 as his pocket allowance. Find his pocket allowance per day.
Options- A. ? 9.5
- B. ? 10.5
- C. ? 12.5
- D. ? 11.5 Discuss
- 5. Sum of three fraction is 2 11/ 24 . If the greatest fraction is divided by the smallest fraction the result is 7/6, which is greater than the middle fraction by 1/3. Find all the three fractions.
Options- A. 3/5, 4/7, 2/3
- B. 7/8, 5/6, 3/4
- C. 7/9, 2/3, 3/5
- D. 7/8, 7/9, 7/10 Discuss
- 6. The Numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator, then find the fraction.
Options- A. 3/7
- B. 4/8
- C. 2/7
- D. 3/8 Discuss
- 7. 783 ÷ 9 ÷ 0.75 =?
Options- A. 130
- B. 124
- C. 118
- D. 116 Discuss
- 8. 4/7 of a pole is in the mud. When 1/3 of it is pulled out, 250 cm of the pole is still in the mud. Find the full length of the pole .
Options- A. 1000
- B. 1100
- C. 950
- D. 1050 Discuss
- 9. The degree f polynomial p(x) = x 3 + 1 + 2x = 6x + 1/x is?
Options- A. 2
- B. 4
- C. 3
- D. 5 Discuss
- 10. If x = 1 + ? 2, then what is the value of x 4 - 4x 3 + 4x 2?
Options- A. -1
- B. 0
- C. 1
- D. 2 Discuss
Decimal Fraction problems
Search Results
Correct Answer:
Explanation:
Let the original fraction be p/q.
Numerator is increased by 200%.
? Numerator = p + 200% of p
= p + 200p/100
= p + 2p
= 3p
and denominator of the fraction is increased by 150%.
Denominator = q + 150q/100
= (100q + 150q)/100
= 250q/100
= 5q/2
Then, according to the question,
3p/5q/2 = 9/35
3p x 2/5q = 9/35
6p/5q = 9/35
? p/q = 9 x 5/35 x 6
p/q = 3/14
Correct Answer: 320
Explanation:
Let the number of pages be p.
Number of pages read on first day = 3p/8
Remaining pages = p - 3p/8 = (8p - 3p)/8 = 5p/8
Number of pages read on second day = 4/5 x 5p/8 = p/2
Now , remaining pages = p - [ 3p/8 + p/2]
= p - [(3p + 4p)/8] = [p- 7p/ 8]
= [(8p - 7p)/ 8] = p/8
According to the question
p/8 = 40
? p = 40 x 8
? p = 320
Correct Answer: 8 cm
Explanation:
Let total length of pencil be x cm.
Then, black part = x/8
Remaining part pencil after black part = x - x/8 = 7x/8
then White part = 1/2 (7x/8)
= 7x/16
Now Remaining part of pencil is blue = total length of pencil - (length of black part + length of white part)
length of blue part of pencil = x - (x/8 + 7x/16)
length of blue part of pencil = x - (2x + 7x)/16
length of blue part of pencil = x - 9x/16
length of blue part of pencil = (16 x - 9x)/16
? Length of blue part = 7x/16;
According to question
Length of blue part = 31/2
7x/16 = 31/2
? 7x/16 = 7/2
? x/16 = 1/2
? x = 16/2
? x = 8 cm
Correct Answer: ? 10.5
Explanation:
Shantanu's pocket allowance = ? 3832.50
Total days in 2011 (general year) = 365 days
Allowance per day = 3832.5/365 = ? 10.5
Correct Answer: 7/8, 5/6, 3/4
Explanation:
Let the greatest, middle and smallest fraction be P, Q and R respectively in decreasing order.
According to the question.
(Greatest fraction) / (Smallest fraction) = 7/6
? P/R = 7/6
? P = 7R/6 ....(i)
and Q = 7/6 - 1/3 = 7 - 2/6 = 5/6 (ii)
Now, P + Q + R = 211/24 (iii )
Substitute the value of P and Q from Eqs. (i), (ii) and put in Eqs (iii), we get
? 7R/6 + 5/6 + R = 59/24
? (7R + 5 + 6R)/6 = 59/24
? (13R + 5) / 6 = 59/24
? 13R = (59/4) - 5 = 39/4
? R = 39 / (4 x 13)
? R = 3/4
On putting the value of R in Eq. (i), we get
P = 7R/6 = (7/6) x (3/4) = 7/8
Correct Answer: 3/7
Explanation:
Let denominator of fraction = x
Then, numerator = x - 4
? Fraction = x - 4/x
Now, according to the question,
8[(x - 4) - 2] = (x + 1)
(x -4) - 2= (x + 1)/8
? x - 6 = x + 1/8
? 8x - 48 = x + 1
? 8x - x = 48 + 1
? 7x = 49
? x = 49/7
? x = 7
? Fraction = (x - 4)/x
Put the value of x.
? Fraction = (7 - 4)/7 =3/7
Correct Answer: 116
Explanation:
? = 783/9 x 0.75 = 116
Correct Answer: 1050
Explanation:
Let us assume length of pole is L.
Length of the pole in Mud is = L x 4/7 = 4L/7
Length of the Pole which is pulled out = L x 1/3 = L/3
Length of the pole is still in mud = Length of the pole in Mud - Length of the Pole which is pulled out
Length of the pole is still in mud = 4L/7 - L/3
According to question,
Length of the pole is still in mud = 250
4L/7 - L/3 = 250
(4L x 3 - L x 7)/7 x 3 = 250
12L - 7L = 250 x 21
5L = 250 x 21
L = 250 x 21/5
L = 50 x 21
L = 1050
Correct Answer: 4
Explanation:
x3 + 1 + 2x =6x + 1/x
x3 + 1 + 2x = (6x2 + 1)/x
(x3 + 1 + 2x)x = 6x2 + 1
x4 - 4x2 - 6x2 -1 =0
x4 - 4x2 + x - 1 =0
Degree of polynomial is highest exponent degree term i.e.,4.
Correct Answer: 1
Explanation:
x = 1 + ?2
? x4 - 4x3 + 4x2 = x2(x2 - 4x + 4)
= x2(x - 2)2
= (1 + ?2)2(1 + ?2 - 2)2
=(?2 + 1)2 (?2 - 1)2
=[(?2)2 - (1)2]2
=(2 - 1)2 =1
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