Q1. Vivek can do a piece of work in 20 and Parth can do it in 25 days. They began together and worked for 5 days. Parth fell ill and left the work. In how many days, Vivek alone can finish the remaining work?
(a) 11
(b) 13
(c) 10
(d) 12
Sol. Vivek’s 1 day work =1/10
Parth’s 1 day work =1/25
Both 1 day work =1/20+1/25=(5 + 4)/100=9/100
Both 5 days work =9/100×5=9/20
Remaining work =1-9/20=11/20 completed by Vivek
∴ Vivek can do 1/20 work = 1 day
∴ Vivek can do 11/20 work =20×11/20 = 11 days
Hence, Vivek alone can finish the remaining work in 11 days.
Q2. By selling a dozen pencils at the cost of Rs. 30, the shopkeeper gains Rs. 10. His percentage of profit was-
(a) 20
(b) 35
(c) 50
(d) 66
Sol. Cost price = (30 – 10) = Rs.20
Percentage profit =(Profit × 100)/(Cost Price )=(10 × 100)/20=50%
Q3. The simple interest on Rs. 300 at the rate of 6% per annum in 2 1/2 yr will be-
(a) Rs. 18
(b) Rs. 36
(c) Rs. 40
(d) Rs. 45
Sol. Interest =(Principal × Rate × Time)/100=(300 × 6 × 5)/(100 × 2)= Rs. 45
Q4. The volume of a cuboid is 440 cm3, the area of its base is 88 cm2, then its height- is
(a) 5 cm
(b) 10 cm
(c) 11 cm
(d) 6 cm
Sol. Volume of cuboid = 440 cm3
Area of its base = 88 cm2
Height =(Volume of the cuboid)/(Area of its base )=440/88=5 cm
Q5. (18 × 72 × 105)/(48 × 315)=√(?) :
(a) 81
(b) 729
(c) 9
(d) 1.732
Sol.
(18 × 72 × 105)/(48 × 315)=√(?)=√(?)=136080/15120=9
9=√(?) ∴ ?=81
Q6. Sum of the interior angles of a regular polygon is 1620°. How many sides does this polygon has?
(a) 11
(b) 10
(c) 12
(d) 9
Sol. Sum of interior angles = (n – 2)×180
∴ (n-2)×180=1620
⇒ 180n – 360 = 1620 ⇒ 180n = 1980
⇒ n=1980/180⇒n=11
Q7. The average age of 14 girls and their teacher’s age is 15 yr. If the teacher’s age is excluded, the average reduces by 1. What is the teacher’s age?
(a) 35 yr
(b) 32 yr
(c) 30 yr
(d) 29 yr
Sol. Total age of 14 girls + 1 teacher = 15 × 15 = 225 yr
Average age of 14 girls = 14 yr
∴ Total age of 14 girls = 14 × 14 = 196 yr
∴ Teacher’s age = 225 – 196 = 29 yr
Q8. If 30% of A = 0.25 of B = 1/5 of C, then A : B : C is equal to –
(a) 5 : 6 : 4
(b) 5 : 24 : 5
(c) 6 : 5 : 4
(d) 10 : 12 : 15
Sol. 30% of A = 25% of B
⇒ 30A = 25B ⇒ A : B = 25 : 30 = 5 : 6
Again 25% of B = 20% of C
⇒ 25B = 20C ⇒ 5B = 4C
⇒ B : C = 4 : 5 ∴ A : B : C = 5 × 4 : 4 × 6 : 6 × 5
= 20 : 24 : 30 = 10 : 12 : 15
Q9. A divisor is 25 times the quotient and 5 times the remainder. The quotient is 16, the divided is –
(a) 6400
(b) 6480
(c) 400
(d) 480
Sol. Divisor = 25 × 16 = 400
Also, divisor = 5 × remainder
∴ Remainder =400/5=80
∴ Divided = Divisor × Quotient + Remainder
= 16 × 400 + 80 = 6480
Q10. Three-fifth of the square of a certain number is 126.15. What is the number?
(a) 210.25
(b) 75.69
(c) 14.5
(d) 145
Sol. Let the number be x
According to the question, x^2×3/5=126.15
⇒ x^2=(126.15 × 5)/3=210.25
∴ x=√210.25=14.5
