1) Four friends (A, B, C and D) started a business in partnership by investing capitals in the proportion 3 : 5 : 4 : 6. During the period of one-year, these capitals were utilized in the proportion of 6 : 4 : 5 : 3 respectively. If, at the end of the year, a profit of Rs. 15,550 was made, what will be the share of D?
a. Rs. 3250.5
b. Rs. 3750
c. Rs. 4062.59
d. Rs. 3682.89
e. None of these
|
Answer
Explanation
|
ANSWER: Rs. 3682.89
Explanation:
A = (Investment * capital utilized) = (3 * 6) = 18
B = (5 * 4) = 20
C = (4 * 5) = 20
D = (6 * 3) = 18
Thus, out of Rs. 76 (18 +20 + 20 + 18), D's share is Rs. 18. Hence, out of Rs. 15,500 the share of D would be given as (18/76) * 15550 = Rs. 3682.89
|
|
2) The value of “A” varies in inverse proportion as the square of “B”. If the value of “A” is equal to 40 when “B” is equal to 12. What would be the value of “A” when “B” is equal to 24 ?
a. 10
b. 15
c. 20
d. 22
e. None of these
|
Answer
Explanation
|
ANSWER: 10
Explanation:
We have, A α 1/B2
A * B2 = K (constant)
When B = 12, A = 40 …..Given
K = 40 * (12)2 = 5760
Now, B = 24. Hence, A = 5760 / 576 = 10
|
|
3) A boy has to cover a total distance of 300 kms. in 6 hours. He travels at the rate of 60 kmph. for first 90 minutes and next 100 kms. at the rate of 50 kmph. At what average speed must he travel now in order to complete the journey in 6 hours?
a. 25 kmph.
b. 32 kmph
c. 44 kmph
d. 58 kmph
|
Answer
Explanation
|
ANSWER: 44 kmph
Explanation:
The boy travels 60 kmph for 90 min, this means he travels 90 km.
Next 100 km at the rate of 50 kmph, this means he travels 100 km.
Total distance traveled till now = 100 + 90 = 190 km
Time spent = 1.5 + 2 = 3.5 hr
Required speed = Remaining distance/ Time
= (300 – 190) /(6 – 3.5)
= 110/ 2.5 = 44 kmph
|
|
4) A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs. 845 in the same period of 2 years, What must be the rate of interest?
a. 5% p.a.
b. 7.5% p.a.
c. 10% p.a.
d. 12.5% p.a.
|
Answer
Explanation
|
ANSWER: 10% p.a.
Explanation:
Given: 800 = (P * R * 2) / 100
S.I. For 1 year = Rs. 400
Thus, (840 – 800) = S.I. on Rs. 400 for 1 year
40 = (400 * R * 1) / 100
R = 10% p.a.
|
|
5) An amount of Rs.20,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
a. Rs. 5000
b. Rs. 4570
c. Rs. 2750
d. Rs. 2950
|
Answer
Explanation
|
ANSWER: Rs. 5000
Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 20,000
Thus we get, 2Q + Q + Q + 4Q = 20,000
8Q = 20,000 or Q = Rs. 2500
Thus, R = Rs. 2500, P = 5000 & S = Rs. 10000
Hence, the required difference = (S – P) = (10000 – 5000) = Rs. 5000
|
|
6) In the quadratic equation ax2 - 11x + 40 = 0, if the sum of two roots is 1.1, what is the product of the two roots?
a. 4
b. 4.2
c. 8
d. None of these
|
Answer
Explanation
|
ANSWER: 4
Explanation:
The sum of the roots of the quadratic equation ax2 - bx + c = 0 are (-b/a) and the product of the roots are (c/a).
Thus, in the equation ax2 - 11x + 40 = 0, where a = a, b = - 11 and c = 40.
we get, sum of the roots = - (- 11) / a = 1.1
a = 11 / 1.1 = 10
Product of the roots = 40 / 10 = 4
|
|
7) For arranging a picnic, each student contributed an amount equal to the number of students while the teacher contributed an amount equal to twice the number of students. However, if each student would have contributed an amount equal to twice the number of students and the teacher would have contributed an amount equal to the number of students, they would have generated Rs. 1056 more. Find the number of students in the group?
a. 24
b. 25
c. 33
d. 50
e. Cannot be determined
|
Answer
Explanation
|
ANSWER: 33
Explanation:
Let the number of students = x. Thus, we get,
[(2x2 + x) – (x2 + 2x)] = 1056
x2 - x - 1056 = 0
Solving the equation, we get, x = 33 or x = - 32.
Since the number of students are to be positive, number of students = x = 33
|
|
8) By giving Rs. 50 to M, A would have the amount equal to what M had earlier. If the sum of the amounts with A and M is Rs. 650. What is the ratio of the amount with A to that with M earlier?
a. 7 : 4
b. 5 : 3
c. 2 : 1
d. 7 : 6
e. 2 : 3
|
Answer
Explanation
|
ANSWER: 7 : 6
Explanation:
Let the amounts with A and M be Rs. “X” and Rs. “Y” respectively.
Thus, we have, X + Y = 650 and
X – 50 = Y
X – Y = 50.
Hence, X = 350 & Y = 300
Thus the required ratio is 350 : 300 = 7 : 6
|
|
9) Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number?
a. 9
b. 12
c. 14
d. 16
e. None of these
|
Answer
Explanation
|
ANSWER: 12
Explanation:
We have, 2/3 * 2/5 * 3/4 * X = 36
X = 180
Now, 4/5 * X = 4/5 * 180 = 144
√144 = 12
|
|
10) The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely?
a. 375
b. 2570
c. 2800
d. 3315
e. None of these
|
Answer
Explanation
|
ANSWER: 3315
Explanation:
Since we require minimum number of square tiles, the size of the tile is given as the H.C.F. of two sides of the room. The H.C.F. Of 1625 cm & 1275 cm. is 25 cms. Hence, we get,
Required Number = (1625 * 1275) / (25 * 25) = 3315
|
|
