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Maths Quiz for KVS and CTET Exams Q1. A and B are two friends. A lives at a place P and B lives at another place Q. Everyday A goes to Q to meet B at 120 km/h. Thus, he takes 3 hours. On a particular day B started to meet A so the he moved towards P. On that day A took only 2 hours to meet on the way instead at Q.  What is the speed of B?
(a) 120 km/h
(b) 80 km/h
(c) 90 km/h
(d) 60 km/h

Q2. A man completes 30 km of a journey at 6 km/hr and the remaining 40 km of the journey in 5 hours. His average speed for the whole journey is:
(a) 70/4 km/hr
(b) 7 km/hr
(c) 15/2 km/hr
(d) 8 km/hr

Q3. Sourav purchased 30 kg of rice at the rate of Rs. 10 per kg and 34 kg at the rate of Rs. 11 per kg. He mixed the two. At what price per kg (in Rs.) should he sell the mixture to make a 30% profit in the transaction?
(a) 12.5
(b) 13
(c) 13.7
(d) 14.25

Q4. The milk and water in two vessels A and B are in ratio 4 : 3 and 2 : 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?
(a) 7 : 5
(b) 5 : 2
(c) 3 : 11
(d) 1 : 2

Q5. A butler wine from a butt of sherry which contained 80% of spirit and he replaced it by wine containing only 32% spirit. Then, the butt was of 48% strength only. How much of the butt did he steal?
(a) 1/4
(b) 3/5
(c) 2/5
(d) 2/3

Q6. 9 years hence, a man will be just 4 times as old as he was 15 years ago. His present age is:
(a) 12 years
(b) 15 years
(c) 16 years
(d) 23 years

Q7. If the four equal circles of radius 3 cm touch each other externally, then the area of the region bounded by the four circles is
(a) 4(9 – ?) sq. cm
(b) 9(4 – ?) sq. cm
(c) 5(6 – ?) sq. cm
(d) 6(5 – ?) sq. cm

Q8. What part of a ditch 48 m long, 16.5 m broad and 4 m deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 m and length 56 m?
(a) 1/9
(b) 2/9
(c) 7/9
(d) 8/9

Q9. Supposing that telegraph poles on a railway track are 50 metres apart. How many pole will be passed by a train in 2 hours. If the speed of the train is 45 km/hr
(a) 1801
(b) 1800
(c) 1601
(d) 1600

Q10. A number of friends decided to go on a picnic and planned to spend Rs. 108 on eatables. Three of them however did not turn up. As a consequence each one of the remaining had to contribute Rs. 3 extra. The number of them who attended the picnic was:
(a) 15
(b) 12
(c) 9
(d) 6

Solutions

S1. Ans.(d)
Sol. Distance between P and Q = 120 × 3 = 360 km
Let the speed of B be S1, then
Time=Distance/Speed
2=360/(120 + S1 )
⇒ S1 = 60 km/h
Here, A and B are moving towards each other. So, the relative speed will be the sum of the speeds of A and B both.

S2. Ans.(b)
Sol. Total distance = (30 + 40)km = 70 km
Total time taken =((30/6)+5)hrs = 10hrs
Average speed =70/10 km/hr = 7 km/hr

S6. Ans.(d)
Sol. Let the present age of the man be x years.
Then, (x + 9) = 4(x – 15)
⇒ 3x = 69
⇒ x =23
Hence, the present age of the man is 23 years.

S7. Ans.(b)
Sol.

Area of the shaded region = Area of square of side
= 36 – (4 × (π ×3^2)/4)
= 36 – 9 ? = 9(4 – ?) sq. cm

S8. Ans.(b)
Sol. Volume of the earth dugout as a tunnel
=πr^2 h= (22/7×2×2×56)=704 m^2
Volume of the ditch = (48×33×4)/2
= (24 × 33 × 4) = 3168 m^3
Part required = 704/3168=2/9

S9. Ans.(a)
Sol. Distance travelled by train in 2 hours = 45 × 2 = 90 kms = 90000 m
No. of pole passed = (90000/50)+1
= 1800 + 1
= 1801 poles

S10. Ans.(c)
Sol.
Let the number of friends be x.
so 108/(x – 3) – 108/x = 3
(108 × 3) /(x(x -3)) = 3
=> x2 – 3x = 108
=> x2 – 12x + 9x – 108 = 0
=> x(x-12)  + 9 (x -12) = 0
(x – 12) (x + 9) = 0
X = 12
Number of friends who attended
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