(a) 38
(b) 45
(c) 57
(d) 66
Q2. 10 women can do a piece of work in 6 days, 6 men can do same work in 5 days and 8 children can do it in 10 days. What is the ratio of the efficiency of a woman, a man and a child respectively?
(a) 4 : 6 : 3
(b) 4 : 5 : 3
(c) 2 : 4 : 3
(d) 4 : 8 : 3
Q3. The ratio of the volume of two cylinders is 7 : 3 and the ratio of their heights is 7 : 9. If the area of the base of the second cylinder is 154 cm2, then what will be the radius (in cm) of the first cylinder?
(a) 6√2
(b) 6√3
(c) 7√2
(d) 7√3
Q4. Kanchan bought a clock with 25% discount on marked price. She sold it with 75% gain on the price she bought. What was her profit percentage on the marked price?
(a) 31.25
(b) 50
(c) 56.25
(d) 60
Q5. A, B and C received an amount of Rs 8400 and distributed among themselves in the ratio of 6 : 8 : 7 respectively. If they save in the ratio of 3 : 2 : 4 respectively and B saves Rs 400, then what is the ratio of the expenditures of A, B and C respectively?
(a) 6 : 8 : 7
(b) 8 : 6 : 7
(c) 9 : 14 : 10
(d) 12 : 7 : 9
Q6. The average age of 24 students is 12 years. It was observed that while calculating the average age, the age of a student was taken as 14 years instead of 8 years. What will be the correct average age (in years)?
(a) 11.25
(b) 11.5
(c) 11.75
(d) 12.25
Q7. 70% of the cost price of an article is equal to the 40% of its selling price. What is the profit or loss percentage?
(a) 63% loss
(b) 70% loss
(c) 75% profit
(d) 80% profit
Q8. a% of b + b% of a = ______
(a) 2a% of b
(b) 2a% of 2b
(c) 2a% of 2a
(d) 2b% of 2b
Q9. If I walk at 7/6 of my usual speed, then I reach my office 15 minutes early. What is the usual time taken (in minutes) by me to reach the office?
(a) 60
(b) 75
(c) 90
(d) 105
Q10. A person lent Rs 10000 to B for 3 years and Rs 6000 to C for 4 years on simple interest at same rate of interest and received Rs 5400 in all from both of them as interest. What is the rate of interest (in %)?
(a) 10
(b) 12.5
(c) 15
(d) 20
Solutions
S1. Ans.(c)
Sol. Total no. which are divisible by 3 = 66
Total no. which are divisible by 3 but not by 7 means which are not divisible by 21= 9
∴ Total number which are divisible by 3 but not by 7 = 66 – 9 = 57
S2. Ans.(d)
Sol. Ratio of total work of women, men and children
= 10×6 : 6×5 : 8×10
= 60 : 30 : 80
∴ Ratio of efficiency
=1/60 ∶1/30 ∶1/80
= 4 : 8 : 3
S3. Ans.(d)
Sol. Let the radius of first and second cylinder be r₁ and r₂ and height be h₁ and h₂ respectively.
∴ ATQ,
(πr_1^2 h_1)/(πr_2^2 h_2 )=7/3
(r_1^2×7)/(r_2^2×9)=7/3⇒(r_1^2)/(r_2^2 )=3⇒r_1=√3 r_2
r_2=r_1/√3…(i)
πr_2^2=154…(ii)
putting value of equation (i) in (ii)
22/7×(r_1^2)/3=154
r₁ = 7√3 cm
S4. Ans.(a)
Sol. Let marked price be Rs. 100.
Therefore, cost price = Rs.75
Selling price=75×175/100=Rs.131.25
∴ Required profit percentage
=(131.25 –100)/100×100
=31.25 %
S5. Ans.(c)
Sol. Amount received by A
=8400×6/21=2400
Amount received by B
=8400×8/21=3200
Amount received by A
=8400×7/21=2800
Saving of A=400/2×3=600
Saving of B = 400
Saving of C=400/2×4=800
Therefore ratio of expenditure
= (2400 – 600) : (3200 – 400) : (2800 – 800)
= 1800 : 2800 : 2000
= 9 : 14 : 10
S6. Ans.(c)
Sol. Total age of 24 student = 24 × 12 = 288
Correct total = 288 – 6 = 282
∴ Correct average=282/24
=11.75
S7. Ans.(c)
Sol. 70% of CP = 40% of SP
SP/CP=7/4
∴ Let CP be 4x and SP be 7x
∴Profit percent=(7x–4x)/4x×100
=3x/4x×100=75%
S8. Ans.(a)
Sol. a/100×b+b/100×a=2ab/100
= 2a% of b
S9. Ans.(d)
Sol. Let the usual speed be 6x km/hr
Therefore, speed at which he reaches 15 min. early is 7x km/hr
∴ ATQ,
d/6x–d/7x=15/60
d/x [1/42]=1/4
d/x=21/2
∴ distance (d)=21/2 x km
∴ usual time=(21/2 x)/6x
=7/4 hours=105 minutes.
S10. Ans.(a)
Sol. ATQ,
(10000×3×R)/100+(6000×4×R)/100=5400
[where R is rate of interest]
30R + 24R = 540
∴R=540/54=10%
