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Maths Questions for DSSSB Exam : 20 March 2018 (Solutions)

Q1. A student obtained equal marks in Physics and Chemistry. The ratio of marks in Chemistry and Math is 2 : 3 and the ratio of marks in Physics and English is 1 : 2. If he has scored an aggregate of 55% marks. The maximum marks in each subject is same. In how many subjects did he score equal to or greater than 60% marks?
(a) 1
(b) 2
(c) 3
(d) 0
Q2. The concentration of glucose in three different mixtures (glucose and alcohol) is     1/2  ,3/5  and  4/5  respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. What is the ratio of glucose and alcohol in the new mixture?
(a) 4 : 5
(b) 3 : 2
(c) 3 : 5
(d) 2 : 3
Q3. 10 years ago the age of Krishna was 1/3 rd of the age of Banshi. 14 years hence the ratio of ages of Krishna and Banshi will be 5 : 9. Find the ratio of their present ages:
(a) 13 : 29
(b) 11 : 27
(c) 29 : 17
(d) 13 : 25
Q4. A dog takes 22 leaps for every 17 leaps of cat and 22 leaps of a dog are equal to 17 leaps of the cat. What is the ratio of the speeds of dog and cat?
(a) 1 : 1
(b) 484 : 289
(c) 17 : 22
(d) 22 : 17
Q5. Mohan Bhai sells chomchome (a favorite indian sweets) at Rs. 15 per kg. A chomchome is madeup of flour and sugar in the ratio of 5 : 3. The ratio of price of sugar and flour is 7 : 3 (per kg). Thus he earns 66 2/3 % profit. What is the cost price of sugar?
(a) Rs. 10/kg
(b) Rs. 9/kg
(c) Rs. 18/kg
(d) Rs. 14/kg
Q6.An amount of money is to be distributed among P, Q and R in the ration 6 : 19 : 7 respectively. If R gives Rs. 200 of his share to Q the ratio among P, Q and R becomes 3 : 10 : 3 respectively. What was the total amount ?
(a) Rs. 6400
(b) Rs.12800
(c) Rs. 3200
(d) Rs. 6800
Q7.Tea at Rs. 126 per kg and at Rs. 135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety (per kg) is
(a) Rs. 169.50
(b) Rs. 175
(c) Rs. 172.50
(d) Rs. 184.5
Q8.A train travels with a speed of 20 m/s in the first 10 minutes, goes 8.5 km in the next 10 minutes, 11 km in the next 10, 8.5 km in the next 10 and 6 km in the next 10 minutes. What is the average speed of the train in kilometer per hour for the journey described ?
(a) 42 kmph
(b) 35.8 kmph
(c) 55.2 kmph
(d) 46 kmph
Q9.19 persons went to a hotel for a combined dinner party. 13 of them spent Rs. 79 each on their dinner and the rest spent Rs. 4 more than the average expenditure of all the 19. What was the total money spent by them ?
(a) Rs. 1536.07
(b) Rs. 1534
(c) Rs. 1492
(d) Rs. 1578.5
Q10.The average weekly salary per head of all employees (supervisors and labourers) is Rs. 100. The average weekly salary per head of all the supervisor is Rs. 600 while the average weekly salary per head of all the labourers is Rs. 75. Find the number of supervisors in the factory if there are 840 labourers in it.
(a) 46
(b) 42
(c) 44
(d) 48
Solutions:
S1. Ans.(b)
Sol. P : C = 1 : 1
C : M = 2 : 3
P : E = 1 : 2
P : C : M : E = 2 : 2 : 3 : 4
Therefore, marks in subjects are 2x, 2x, 3x & 4x.
A/q,   (2x+2x+3x+4x)/4 = 55
x=20
So, marks in Physics = 40
Marks in chemistry = 40
Marks in math = 60
Marks in English = 80
S2. Ans.(b)
Sol. Concentration of glucose are in ratio = 1/2:3/5:4/5
Quantity of glucose taken from A = 1 litre out of 2 litre.
Quantity of glucose taken from B = 3/5×3=1.8  lt.
Quantity of glucose taken from C = 0.8 lt.
So, total glucose taken out from A, B & C, = 3.6 lt.
So, quantity of alcohol = (2 + 3 + 1) – 3.6 = 2.4 litre.
Ratio of glucose to alcohol = 3.6/2.4 = 3:2
S3. Ans.(a)
Sol. Let 10 years ago Krishna’s age = x years.
Let 10 years ago Banshi’s age = 3x years
A/q,
(x+10+14)/(3x+10+14) = 5/9
x= 16 years
So, their present age = 16 + 10 = 26 years
& 16 × 3 + 10 = 58 years.
Ratio = 13 : 29
S4. Ans.(a)
Sol. Ratio of speed of dog & cat =
22/22 : 17/17  = 1:1
S5. Ans.(d)
Sol. S.P. = 15 per kg.
Profit = 66 2/3 %
C.P. = (15×100×3)/500 = Rs. 9
Now, flour : sugar  = 5 : 3
So in 1 kg = flour = 625 gm.
& Sugar = 375 gm.
Let price of sugar = 7x
Flour = 3x
According to question,
625/1000 ×3x+  375/1000 ×7x=9
x=2
So, C.P. of sugar = 7 × 2 = 14 Rs./k…..g.
S6. Ans.(a)
Sol.
Let shares of P, Q and R be 6x, 19x and 7x respectively.
6x : 19x+200 : 7x–200
3 10 : 3
⇒ 19x + 200 = 10/16  ×32x
⇒ x = 200
∴ Total amount = 6400
S7. Ans.(d)
Sol.
Let price of third variety be Rs. x per kg.
∴  1/5×126+2/5×135+2/5× x=1×153
⇒ 396 + 2x = 765
⇒ x = 184.5
S8. Ans.(c)
Sol.
Average speed=(Total distance)/(Total time)
=(20×10/60×18/5+8.5+11+8.5+6)/(10+10+10+10+10)×60
= 55.2 kmph
S9. Ans.(a)
Sol.
Let average expenditure was Rs. x
13 × 79 + 6 × (x + 4) = 19x
⇒ x = Rs. 80.84
∴ Total money = 19 × 80.84
= 1536.07 rupees
S10. Ans.(b)
Sol.
Let no. of supervisors = x
∴ 600x + 75 × 840 = (x + 840) × 100
⇒ 500x = 21000
⇒ x = 42