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Maths Questions for DSSSB Exam : 8 March 2018 (Solutions)

Maths Questions for DSSSB Exam : 8 March 2018 (Solutions)_30.1
Q1. Akshar, Akshay, and Akshat have to read a document of seventy eight pages and make a presentation next day. They realize that the article is difficult to understand and they would require team work to finish the assignment. Akshar can read a page in 2 min, Akshay in 3 min, and Akshat in 4 min. If they divide the article into 3 parts so that all three of them spend the equal amount of time on the article, the number of pages that Akshay should read is 
(a) 24
(b) 25
(c) 26
(d) 27
Q2. Three pipes A, B and C can fill a tank in 15 minutes, 20 minutes and 30 minutes respectively. All three pipes started to fill the tank at same time. The pipe C is closed 6 minutes before the tank is filled. In what time the tank will be full?
(a) 6 minutes
(b) 8 minutes
(c) 12 minutes
(d) 14 minutes
Q3. In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Arun?
(a) 67 kg
(b) 69 kg
(c) 71 kg
(d) 74 kg
Q4. An alloy contains only zinc and copper. One such alloy weighing 15 gm contains zinc and copper in the ratio of 2 : 3 by weight. If 10 gm of zinc is added then find what amount of copper has to be removed from the alloy such that the final alloy has zinc and copper in the ratio of 4 : 1 by weight?
(a) 5 gm
(b) 5.5 gm
(c) 6 gm
(d) 4.8 gm
Q5. Two men A and B working together complete a piece of work which it would have taken them 30 and 40 days respectively to complete if they worked separately. If they received a payment of Rs. 2100, B’s share is: 
(a) Rs. 900 
(b) Rs. 800 
(c) Rs. 1200 
(d) Rs. 1300
Q6. Three men A, B and C start a business together. They invest Rs 30000, Rs 24000 and Rs 42000 respectively in the beginning. After 4 months, B took out Rs 6000 and C took out Rs 10000. They get a profit of Rs 11960 at the end of the year. B’s share in the profit is (approximately)
(a) Rs 2700
(b) Rs 2803
(c) Rs 2900
(d) Rs 2785
Q7. A, B and C started a business in a partnership with investment of Rs 12000, Rs 26000 and Rs 32000 respectively. After 4 months A leaves. After 6 months B leaves and A joines with an amount equal to his earlier investment. After 10 months, C leaves and B joins with his prior investment. At the end of the year they earn a profit of Rs 53622. Find the share of B in the annual profit.
(a) Rs 17221
(b) Rs 17212
(c) Rs 17222
(d) Rs 18212
Q8. The ratio between the angles of a quadrilateral is 3 : 4 : 6 : 7. Half of the second largest angle of the quadrilateral is equal to the smaller angle of a parallelogram. What is the value of adjacent angle to the smaller angle of the parallelogram ?
(a) 136°
(b) 126°
(c) 94°
(d) 96°
Q9. Ram’s present age is three times his son’s present age and two fifth of his father’s present age. The average of the present age of all of them is 46 years. What is the difference between Ram’s son’s present age and Ram’s father’s present age ? 
(a) 68 years
(b) 88 years
(c) 58 years
(d) 78 years
Q10. Average score of Rahul, Manish and Suresh is 63. Rahul’s score is 15 less than Ajay and 10 more than Manish. If Ajay scored 30 marks more than the average score of Rahul, Manish and Suresh. What is the sum of Manish’s and Suresh’s scores ? 
(a) 120
(b) 111
(c) 117
(d) Cannot be determined 
Solutions:
S1. Ans.(a)
Sol.
Ratio of their efficiency = 6:4:3
∴ Pages read by Akshay = 4/13×78=24 pages 
S2. Ans.(b)
Sol.
Work done in last 6 minutes = 6×(1/15+1/20)=42/60
remaining work = 1-42/60=18/60
per minute work of A, B and C together = 1/15+1/20+1/30=9/60
Total no. of minutes = (18/60)/(9/60)+6=8 minutes
S3. Ans.(a)
Sol.
Let Arun’s weight be X kg. 
According to Arun, 65 < X < 72
According to Arun’s Brother, 60 < X < 70
According to Arun’s Mother, X ≤ 68 
The values satisfying all the above conditions are 66, 67 and 68
∴ Required average=(66+67+68)/3=67 kg
S4. Ans.(a)
Sol. 1st alloy zinc = 2/5 × 15 = 6 gm
Copper = 3/5 × 15 = 9 gm
Let copper to be removed = x
Then,
(6+10)/(9-x)=4/1
⇒ 16 = 36 – 4x
⇒ x = 5 gm
S5. Ans.(a)
Sol.
A and B can complete the work in 30 and 40 days respectively.
So, ratio of their wages =1/30:1/40=40∶30
∴ Share of B =30/(40+30)×2100=Rs 900
S6. Ans.(b)
Sol.
(A’s profit) : (B’s profit) : (C’s profit) 
= (30,000 × 12) : (24,000 × 4 + 18,000 × 8) : (42,000 × 4 + 32,000 × 8)
= 30 × 12 : (24 × 4 + 18 × 8) : (42 × 4 + 32 × 8) 
= 45: 30 : 53 
∴B’s profit=30/128×11960 =2803.125
≈ 2,803 (approximately) 
S7. Ans.(b)
Sol.
(A’s profit) : (B’s profit) : (C’s profit) 
= (12,000 × 4 + 12,000 × 6) : (26,000 × 6 + 26,000 × 2) : (32,000 × 10) 
= 12,000 × 10 : 26,000 × 8 : 32,000 × 10 
= 15 : 26 : 40 
∴ Share of B in total profit=26/(15+26+40)×53622
=Rs.17,212 
S8. Ans.(b)
Sol.
Sum of all angles of quadrilateral = 360 
⇒ 3x + 4x + 6x + 7x = 360 
⇒ x = 18 
∴ Second largest angle = 6 ×18 
= 108 
∴ adjacent angle of parallelogram
=180-108/2=126°
S9. Ans.(d)
Sol.
Let Ram’s present age is x years. 
⇒(x+x/3+5/2 x)/3=46 
⇒x=36 years. 
∴Required difference=5/2×36-36/3=78 years 
S10. Ans.(b)
Sol.
Ajay’s score = 63 + 30 = 93 
Rahul’s score = 93 – 15 = 78 
Manish’s score = 78 – 10 = 68 
∴ Suresh’s score = 63 × 3 – (68 + 78) = 43
∴ Required sum = 68 + 43 = 111