Q1. A can complete a piece of work in 10 days. B is 33.33% less efficient than A. calculate the number of days required to both to complete the work.
(a) 8 days
(b) 6 days
(c) 12 days
(d) 10 days
Q2.A, B and C are three friends. They invested certain amount in the ratio 1 : 2 : 3 and the ratio of investment at the end of year is 3 : 8 : 18. Calculate the ratio of time for which they invested.
(a) 3 : 4 : 6
(b) 4 : 5 : 6
(c) 6 : 7 : 8
(d) 7 : 8 : 9
Q3.Calculate the total Total Surface Area (TSA) of cone whose radius is 3 cm and height is 4 cm.
(a) 24π cm²
(b) 25π cm²
(c) 28π cm²
(d) 20π cm²
Q5.If the difference between CI and SI for 3 years is Rs. 31. Calculate the principle if rate of interest is 10%.
(a) Rs. 1000
(b) Rs. 1500
(c) Rs. 2000
(d) Rs. 800
Q6. The simple interest accrued on a sum of certain principal is Rs. 5,400 in 3 yr at the rate of 18% per annum. What would be the compound interest accrued on that principal at the rate of 10% per annum in 2 yrs.?
(a) Rs. 2,000
(b) Rs. 2,150
(c) Rs. 1,800
(d) Rs. 2,100
Q7. If the numerator of a fraction is increased by 250% and the denominator is increased by 150%. The resultant fraction is what percent of original fraction?
(a) 142%
(b) 135%
(c) 140%
(d) 130%
Q8. One of the angles of a quadrilateral is twice the smaller angle of a rhombus. The respective ratio between the adjacent angles of the rhombus is 5 : 4. Remaining three angles of the quadrilateral are in the ratio 13 : 17 : 10 respectively. What is the sum of the second largest and the smallest angles of the quadrilateral?
(a) 155°
(b) 125°
(c) 135°
(d) 140°
Q9. An urn contains 4 coins of one rupee and 3 coin of two rupee . If three coins are picked at random, what is the probability that two are of one rupee and one is of two rupee coin?
(a) 13/35
(b)19/35
(c) 17/35
(d) 18/35
Q10. The sum of five numbers is 924. The average of first two numbers is 201.5 and the average of last two numbers is 196. What is the third number?
(a) 133
(b) 129
(c) 122
(d) Cannot be determined
Solutions:
S1. Ans.(b)
Sol.
A = 10
Ratio of efficiency of A and B
3 : 2
∴ B will complete the work in 15 days.
Required days=(A×B)/(A+B)
=(10×15)/(10+15)=6 days
S2. Ans.(a)
Sol.
Ratio of Investment = 3 : 8 : 18
Ratio of Amount = 1 : 2 : 3
∴ Ratio of time
3/1 ∶8/2 ∶18/3
= 3 : 4 : 6
S3. Ans.(a)
Sol.
Radius (R) = 3
Height (h) = 4
Slant height =√(h^2+r^2 )
(ℓ) = √(3^2+4^2 )
ℓ = 5 cm
TSA = πrℓ + πr²
= πr (ℓ + r)
= π×3 (5 + 3)
= 24 π cm²
S5. Ans.(a)
Sol.
C.I. – S.I. = 31 Rs.
R = 10%
For 3 yr.
CI – SI =P(R/100)^2 ((300+R)/100)
31=P(10/100)^2 (310/100)
P = Rs. 1000
S6. Ans.(d)
Sol.
Sum = (5400×100)/(18×3)
= 10,000
∴ C.I. =10,000 (1+10/100)^2-10,000
= 12,100 – 10,000
= 2,100
S8. Ans.(c)
Sol.
Angles of rhombus
=5/9×180,4/9×180
= 100°, 80°
Let remaining angles of quadrilateral are 13x, 17x and 10x respectively
∴ 13x + 17x + 10x = 360 – 160
= 200
⇒ x = 5
∴ Required sum = 50 + 17 × 5
= 135°
S10. Ans.(b)
Sol.
Third number= 924 – (2 × 201.5 + 2 × 196)
= 924 – 795
= 129
