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# Maths Questions for DSSSB Exam (Solutions)

Q1.A man can swim at 9 kmph in still water. He covers 21 Km distance in upstream and 21 Km distance in downstream in total 7 hours. Find the speed of stream of river.
(a) 2√3 km/h
(b) 3√3 km/h
(c) 3 km/h
(d) 4 km/h
Q2.The present population of a city is 52,650. What was the population of the city two years ago, if the population reduces at the rate of 10% per annum?
(a) 65,000
(b) 50,000
(c) 55,000
(d) 62,000
Q4.The compound interest for two years on a certain sum at certain rate is equal to the simple interest accrued on the same sum at the rate of 11% for four years. What is the rate of compound interest?
(a) 25%
(b) 20%
(c) 30%
(d) 35%
Q5.A person covers a total distance of 135 km in 9 hours. He covers some part of journey by ola cab with a speed of 21 km/h and rest part of Journey by e-rikshaw with a speed of 14km/h. What distance he covered by e-rikshaw?
(a) 110 km
(b) 106 km
(c) 105 km
(d) 108 km
Q6. Amit spends 70% of his income. If his income was increased by 25% and he increased his expenditure by 20%, by how percent his saving increased?
(a) 25%
(b) 34.56%
(c) 36.67%
(d) 40%
Q7. A vendor bought 7 lemons in Rs. 2. To get a profit of 40%, at what rate he will sell these lemons?
(a) 2 in Rs. 1
(b) 3 in Rs.2
(c) 5 in Rs. 2
(d) 12 in Rs.5
Q8. In how many ways the word ‘SPECIES’ can be arranged such that P and C are always at two ends?
(a) 120
(b) 60
(c) 30
(d) 50
Q9. In a basket there are 2 red, 5 green and 4 white flags , 3 flags are selected randomly. Find the probability that two are green and one is red.
(a) 4/33
(b) 5/33
(c) 29/33
(d) 1/33
Q10. A, B and C start a business together by investing a total amount of 60,000. Sum of A is Rs. 5,000 more than that of B and sum of B is Rs. 8,000 more than that of C. If total profit at the end of a year was found to be Rs. 45,000, what is the share of B in the profit?
(a) Rs. 14,750
(b) Rs. 15,750
(c) Rs. 13,600
(d) Rs. 16,470
Solutions:
S1. Ans.(b)
Sol.
Let speed of stream = s kmph
∴21/(9 –s)+21/(9+s)=7
⇒ 3 × (9 + s + 9 – s) = (81 – s²)
⇒ s² = 27
⇒ s = 3√3 kmph
S2. Ans.(a)
Sol.
Required population
=52,650/(1 –10/100)^2
=(52,650×100)/81
=65,000
S3. Ans.(c)
Sol.
Height of cone
=2/5×(11×2+13)
= 14 cm
∴ volume of cone
=1/3×22/7×225/4×14
= 825 〖cm〗^3
S4. Ans.(b)
Sol.
Let rate of C.I. = r % per annum
∴(P×11×4)/100=P[(1+r/100)^2–1]
⇒144/100=(1+r/100)^2
⇒1+r/100=1.2
⇒ r = 20%
S5. Ans.(d)
Sol.
Let he covers x km by e-rikshaw.
∴x/14+(135 –x)/21=9
⇒ 3x + 270 – 2x = 9 × 42
⇒ x = 108 km
S6. Ans.(c)
Sol.
Initial savings = 100 – 70 = 30%
New savings
=125 –70×120/100
= 41%
∴ Required percentage
=(41–30)/30×100
=110/3%
≈ 36.67%
S7. Ans.(c)
Sol.
Selling price of each lemon
=2/7×140/100
=2/5
i.e. 5 lemons in Rs. 2
S8. Ans.(b)
Sol.
2S, 2E, P, C, I
Required ways=5!/(2!×2!)×2!
=60
S10. Ans.(b)
Sol.
Let C’s investment = Rs. x
∴ x + (x + 8000) + (x + 8000 + 5000) = 60,000
⇒ 3x = 39,000
⇒ x = 13,000
∴ Ratio of their investments
= 26000 : 21000 : 13000
= 26 : 21 : 13
∴ B’s share in profit
=21/60×45000
= 21× 750
= Rs. 15,750