Maths Questions for DSSSB Exam : 30th May 2018 (Solutions)

previous years maths questions of ctet exam

Q1. King Dashratha, at his eleventh hour, called his three queens and distributed his gold in the following way: He gave 50%  of his wealth to his  first wife, 50% of the rest to his second wife and again 50% of the rest to his third wife. If their combined share is worth, 1,30,900 kilograms of gold, find the quantity of gold King Dashratha was having initially? 
(a) 1,50,000 kg 
(b) 1,49,600 kg 
(c) 1,51,600 kg 
(d) 1,52,600 kg 
Q2. A dog after travelling 50 km meets a swami who counsels him to go slower. He then proceeds at 3/4 of his former speed and arrives at his destination 35 minutes late. Had the meeting occurred 24 km further the dog would have reached its destination 25 minutes late. The speed of the dog is  
(a) 48 km/h
(b) 36 km/
(c) 54 km/h 
(d) 58 km/h 
Q3. Length of a rectangular field is increased by 14 metres and breadth is decreased by 6 metres, area of the field remains unchanged. If length be decreased by 14 metres and breadth be increased by 10 metres, again area remains unchanged. Find the perimeter of the rectangle.
(a) 172 m
(b) 192 m
(c) 162 m
(d) Data inadequate
Q4. If A and B working separately can do a piece of work in 8 and 12 hours respectively. If they work alternatively every hour starting with A at 9 a.m., when will be the work completed?
(a) 6 pm
(b) 6 : 30 pm
(c) 5 pm
(d) 5 : 30 pm
Q5. A bus meets with an auto at 10:00 am while going the same way in the same direction towards Haridwar. The Bus reaches at Haridwar at 12:30 p.m. and take 1 hour rest at there. Bus return on the same way and meet with the same auto half an hour later. At what time the auto will reach at Haridwar?
(a) 3 pm
(b) 4 pm
(c) 3:30 pm
(d) 5 pm 
Q6. When a cycle manufacturer reduced selling price of cycle by 50%, the number of bicycles sold radically increased by 600%. Initially the manufacturer was getting only 140% profit. What is the percentage increase of his profit?
(a) 10%
(b) 14%
(c) 0%
(d) Cannot be determined
Q7. A pump can be operated both for filling a tank and for emptying it. The capacity of tank is 2400 m^3. The emptying capacity of the pump is 10 m^3 per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank than to fill it. Find the filling capacity of the pump. 
(a) 45 m^3/minute
(b) 30 m^3/minute
(c) 50 m^3/minute
(d) 55 m^3/minute
Q8. A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. He also uses a 900 gram weight instead of a 1 kilogram weight. Find his percentage profit due to these due to these maneuvers.
(a) 8%
(b) 12%
(c) 20%
(d) 16%
Q9. Krishna can do a work in 10 days while Mohan can do the same work in 20 days. They started work together. After 3 days Krishna left the work and Mohan completed it. How many days Mohan worked alone more than the number of days required when both work together to complete the work ?
(a) 4 1/3
(b) 3 1/4
(c) 2 3/5
(d) 3 2/3
Q10. The cost price of three varieties of apples namely A, B and C is Rs. 20/kg, Rs. 40/kg and Rs. 50/kg respectively. Find the selling price of one kg of apple in which these three varieties of apples are mixed in the ratio of 2 : 3 : 5 such that there is a net profit of 20% ? 
(a) Rs. 48 
(b) Rs. 48.6
(c) Rs. 49.2
(d) Rs. 49.8 
Solutions:
S1. Ans.(b)
Sol.
Let king has total 100% gold.
So, 
50% + 25% + 12.5% = 130900
87.5% = 130900
or 7/8=130900
So, 100% =130900×8/7
= 149,600 kg
S3. Ans.(a)
Sol.
Let the length of the rectangle is l and breadth is b
(l+14)(b-6)=lb
7b-3l=42 ………….(i)
(l-14)(b+10)=lb  
5l-7b=70 ………………(ii)
from eqn. (i) and (ii)
l=56 
 b=30
 Perimeter =2(l+b)
=2(56+30) 
=172 m
S4. Ans.(b)
Sol.
Works completed in first 2 hour = 1/8+1/12
= 20/96
Work completed in 8 hours = 4×20/96=80/96
Work completed in 9 hours = 1/8+80/96=92/96
Now it’s B’s turn who work 1/12 or 8/96 per hour 
Work remaining = 1-92/96=4/96
So remaining work will be completed in 4/(96/(8/96)) = 1/2 hour
Total time = 9 1/2 hour or 6 : 30 pm
S6. Ans.(c)
Sol. 
Let C.P of 1 cycle = Rs 100
∴ S.P. of 1 cycle =Rs 240
New S.P. of 1 cycle =240/2=Rs 120
No. of cycles sold now = 7
∴ total new S.P. = 120 ×7 =Rs 840
Total C.P. = 700
∴ Profit remains same
S7. Ans.(c)
Sol.
Let filling capacity be x m^3/min 
So, emptying capacity = (x+10) m^3/min
According to question
2400/x-2400/(x+10)=8  
⇒ 2400((x+10-x)/x(x+10) )=8 
⇒ x^2+10x-3000=0 
⇒ x=50 m^3/min
S8. Ans.(c)
Sol.
Profit after giving discount = 20-10-200/100=8%
∴ Overall profit = (108×1)/0.9-100=18/0.9=20%
S9. Ans.(a)
Sol. Let total work = 100
Krishna’s efficiency = 10%
Mohan’s efficiency = 5%
Work done by Krishna and Mohan together in 3 days
= 15 × 3 = 45%
Now, Number of days in which Mohan completed rest (55%) work alone =55/5=11
Now number of days Krishna and Mohan both worked together = 100/15=6 2/3
∴Required difference in number of days =(11)-(6 2/3)
=13/3=4 1/3days
S10. Ans.(c)
Sol.
Total C.P. of mixed varities = 20×2+40×3+50×5 
= Rs. 410 
∴price per kg = Rs. 41
So, required S.P. = 120/100×41= Rs. 49.2 
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