Q1. A person distributes his pencils among four friends A, B, C, D in the ratio 1/3 ∶1/4 ∶1/5 ∶1/6. What is the total number of pencils that the person should have?
(a) 57
(b) 65
(c) 75
(d) 45
Q2. If A = 2/3 of B and B = 4/5 of C, then A : B : C is
(a) 12 : 8 : 10
(b) 15 : 10 : 8
(c) 10 : 15 : 12
(d) 8 : 12 : 15
Q3. Two equal maximum sized circular plates are cut off from a circular paper sheet of circumference 352 cm. Then the circumference of each circular plate is
(a) 176 cm
(b) 150 cm
(c) 165 cm
(d) 180 cm
Q4. The inradius of an equilateral triangle is √3 cm, then the perimeter of that triangle is
(a) 18 cm
(b) 15 cm
(c) 12 cm
(d) 6 cm
Q5. The difference between the circumference and diameter of a circle is 150 m. The radius of that circle is (Take π=22/7)
(a) 25 metre
(b) 35 metre
(c) 30 metre
(d) 40 metre
Q6. The perimeters of a circle, a square and an equilateral triangle are same and their areas are C, S and T respectively. Which of the following statement is true?
(a) C = S = T
(b) C > S > T
(c) C < S < T
(d) S < C < T
Q7. A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
(a) 36
(b) 38
(c) 40
(d) 42
Q8. The least five-digit perfect square number which is divisible by 3, 4, 5, 6, 8 is
(a) 14400
(b) 10800
(c) 10200
(d) 32400
Q9. From a vessel containing 100L of wine, 10L are drawn out and an equal amount of water is added. From the mixture, 10L is again drawn out and same quantity of water is added. What is the final ratio of wine to water?
(a) 90:10
(b) 91:9
(c) 81:19
(d) 80:20
Q10. What will be the remainder when (67^67 + 67) is divided by 68?
(a) 1
(b) 63
(c) 66
(d) 67
Solutions
S1. Ans.(a)
Sol. A : B : C : D = 1/3 ∶1/4 ∶1/5 ∶1/6
= 20 : 15 : 12 : 10
= 57
S2. Ans.(d)
Sol. A : B = (2 : 3) ×4
B : C = (4 : 5)×3
A : B : C = 8 : 12 :15
S4. Ans.(a)
Sol. Inradius of equilateral triangle =side/(2√3)
√3=side/(2√3)
side = 6 cm
perimeter of an equilateral triangle = 3 × 6 = 18 cm
S5. Ans.(b)
Sol. Circumference of circle = πd
∴ πd – d = 150
d(π – 1) = 150
d(22/7-1)=150
d×(15/7)=150
d=(150×7)/15=70
Radius =d/2=70/2
= 35m
S7. Ans.(c)
Sol. Let the mother’s present age be x years
Then, the person’s present age = (2 x /5) years
Therefore, (2 x /5) + 8 = ½(x+8)
x= 40 years.
S8. Ans.(a)
Sol. LCM of 3,4,5,6 and 8 = 120. Now, by seeing the option,
we get that 14400 is least five-digit perfect square number which is divisible by 120.
S10. Ans.(c)
Sol. (x^n +1) will be divisible by (x+1) only when n is odd.
So, (67^,67 + 1) + 66, when divided by 68 will give 66 as remainder.
