Q1. A man takes 6 h 15 min in walking a distance and riding back to the starting place. He could walk both ways in 7 h 45 min. The time taken by him to ride the ways is
(a) 4 h
(b) 4 h 30 min
(c) 4 h 45 min
(d) 5 h
Q2. In a race of 1000 m, A can beat B by 100 m. In a race of 400 m, B beats C by 40 m. In a race of 500 m A will beat C by
(a) 95 m
(b) 50 m
(c) 45 m
(d) 60 m
Q3. Mr. Saxena started a business by investing Rs. 50000. Four months later, Mr. Jain joined the business by investing Rs. 90000. If the profit at the end of the year was Rs. 22000, then how much amount would Mr. Jain have received as the profit?
(a) Rs. 16000
(b) Rs. 14000
(c) Rs. 12000
(d) Rs. 11000
Q4. Rs.700 is divided among A, B and C so that A receives half as much as B and B half as much as C. Then C’s share is:
Q5. A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, then how much C must pay as his share of rent?
(a) Rs. 45
(b) Rs. 50
(c) Rs. 55
(d) Rs. 60
Q6. What is the least number of soldiers in a regiment, such that they stand in rows of 18, 15 and 25 and also from a solid square?
Q7. A can do a work in 12 days and B does the same work in 18 days. Efficiency of C is 3/2 times the efficiency of A. in how many days, all of them working together will do the job?
(a) 3.8 days
(b) 4 days
(c) 3 days
Q8. A is 40% more efficient than B, and B is 20% less efficient than C. If A can do a work in 50 days. In how many days all of them together can do the whole work?
(a) 19.17 days.
(b) 6 days
(c) 12 days
(d) 30 days
Q9. A and B together can do a work in 12 days, B and C together can do the same work in 10 days and A and C together can do the same work in 8 days. In how many days will the work be complete if A, B and C are working together?
(a) 6.48 days
(b) 7.2 days
(c) 6 days
(d) 5 days
Q10. A bag contains Rs 216 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 2 : 3 : 4. The number of 50 paise coins is:
Sol. Time taken in walking both way
= 7 h 45 min …(i)
Time taken in walking one way and riding back
= 6h 15 min …(ii)
On multiplying equation (ii), by 2, then
Subtracting it from equation (i) we get
Time taken by the man to ride both ways
= 12 h 30 min – 7 h 45 min
= 4 h 45 min
Sol. According to the question,
When A runs 1000 m, B runs 900 m
When A runs 500 m, B runs 450 m
Again, when B runs 400 m, C runs 360 m
When B runs 450 m, C runs
=(360/400)×450 = 405 m
∴ Required distance
= 500 – 405 = 95 m
Sol. Ratio of their investments
= (50000 × 12): (90000 × 8) = 5: 6
∴ Amount received by Mr Jain
= (6/11) × 22000 = Rs. 12000.
Sol. Let C’s share = Rs.x. Then
B’s share = Rs.x/2
And, A’s share = Rs.x/4
A: B:C = x/4:x/2:x=1:2:4
Hence, C’s share = Rs.700×(4/7) = Rs.400
Sol. A, B and C pay in the ratio of
10 × 7 : 12 × 5 : 15 × 3
∴ C pay Rs. 9/35 × 175 = Rs. 45.
Sol. Number of soldiers should be a multiple of 18, 15 and 25 ⇒ Number should be a multiple of LCM (18, 15, 25)
Now lowest multiple of 450 that is a perfect square = 900. Hence option (c) is the answer.
Sol. A in one day =1/12
B in one day =1/18
C’s efficiency =3/2 A
C in one day =3/2×1/12=1/8
Hence, C will take = 8 days to do the work.
all of them working together will do the job=72/6+4+9=3.8 days
Sol. A does the work in 50 days and A is 40% more efficient that B ⇒ B will take 70 days to finish the same work
B takes 70 days to finish the work and B is 20% less efficient than C ⇒ C is 25% more efficient than B ⇒ C will take 70/1.25 = 56 days to finish the work.
Let us assume the LCM of 70, 50 and 56 = 1400 units of work to be done.
Work done by A/day =1400/50 = 28 units
Work done by B/day =1400/70 = 20 units
Work done by C/day = 25 units
Work done by all of them together/day = 73 units
Time required to finish the work = 1400/73 = 19.17 days.
Sol. Let us assume work = LCM of (12, 10, 8) = 120 units
So, A and B are doing 10 units in one day B and C are doing 12 units in a day and A and C are doing 15 units in a day.
Adding all these, 2(A + B + C) are doing 37 units in a day.
⇒ (A + B + C) are doing 37/2=18.5 units in a day.
So, time taken to complete the work =120/18.5 days = 6.48 days
Sol. Let number of one-rupee coins = 2 K
Number of 50-paise coins = 3 K
Number of 25-paise coins = 4 K
2K × Rs. 1 + 3 K × Rs. 0.5 + 4K × Rs. 0.25 = Rs. 216
⇒ 2 K + 1.5K + K = 216
The number of 50 paise coins=3K=144