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# Maths Questions for HTET,KVS Exam : 15th December 2018 (Solutions)

Q1. The simple interest on a sum for 5 years is Rs 16800. The rate of interest for the first 3 years is 8% per annum and for the next 2 years is 12% per annum. What is the value (in Rs) of sum?
(a) 30000
(b) 38000
(c) 32000
(d) 35000
Q2. Selling price of an article is Rs 1144. If loss percentage is 12%, then what is the cost price (in Rs) of article?
(a) 1300
(b) 1006
(c) 1242
(d) 1440
Q3. Marked price of a chair is Rs 800 and discount is 15%. What is additional discount (in percentage) should be offered to the customer to bring the price of chair to Rs 578?
(a) 15
(b) 10
(c) 16.5
(d) 17.5
Q5. Two pipes can fill a cistern in 28 and 21 hours respectively and an another pipe can empty 30 gallons of water per hour. All the three pipes working together can fill the empty cistern in 84 hours. What is the capacity (in gallons) of the cistern?
(a) 350
(b) 450
(c) 420
(d) 480
Q6. A train is moving at the speed of 36 km/hr. How many seconds it will take to cover a distance of 600 meters?
(a) 60
(b) 120
(c) 30
(d) 40
Q7.The area of a square is 40.5 cm². Find the length of its diagonal (in cm).
(a) 9
(b) 4 .5
(c) 18
(d) 13 .5
Q8. What is the measure of an exterior angle of a regular polygon of 10 sides?
(a)30
(b) 24
(c) 36
(d) 20
Q9. The total surface area of a hemisphere is 462 cm2. Find its diameter (in cm).
(a) 7
(b) 2 8
(c) 21
(d) 14
Q10.Determine the value of ‘x’, if x = ((943+864)²-(943-864)²)/((1886×1728))
(a) 1
(b) 4
(c) 79
(d) 1789
Solutions:
S1. Ans.(d)
Sol.
(P×3×8)/100+(P×2×12)/100=16,800
12P = 16800 × 25
⇒ P = 35000
S2. Ans.(a)
Sol.
We have, SP = Rs. 1144
CP = 1144/88×100=  Rs. 1300
S3. Ans.(a)
Sol.
SP after 15% discount = 800 × 85/100=680
Required discount = 102/680×100 = 600/400=15%
S6. Ans.(a)
Sol.
Speed of train = 36 km/h = 36 ×5/18 = 10 m/s
Req. time = 600/10=60 sec.
S8. Ans.(c)
Sol.
Measure of an exterior angle
= 360/n = 360/10=36°
S9. Ans.(d)
Sol.
Total surface area of the hemisphere = 462
⇒ 3πr² = 462
⇒  πr² = 154
⇒ r = 7cm
Diameter = 2r  = 14 cm
S10. Ans.(a)
Sol.
Let, 943 = a & 864 = B
Given,
x=((a+b)²-(a-b)²)/(2a×2b)=(a²+b²+2ab-(a²+b²-2ab))/4ab
=4ab/4ab=1