Model Questions on Math SET 1 with solution for TA written Exam

Model Paper of Math SET 1

1. The average age of 40 boys in a class is 15. The average age of a group of 18 boys in the class is 16 and the average age of another 12 boys in the class is 14. What is the average age of the remaining boys in the class?
(1) 15•25 years
(2) 14.4 years
(3) 14•75 years
(4) None of these

2. Ruby invested an amount of Rs. 5,800 for 2 years. At what rate of compound interest will she get an amount of Rs. 6394•5 at the end of two years ?
(1) 5 p.c.p.a.
(2) 4 p.c.p.a.
(3) 6 p.c.p.a.
(4) 8 p.c.p.a.

3. A boat covers a distance of 30 km downstream in 2 hours while it takes 6 hours to cover the same distance upstream. How much time the boat will take to cover 90 km in still water?
(1) 6 hrs
(2) 9 hrs
(3) 15 hrs
(4) None of these

4. A lent Rs 5000 to B for 2 years and Rs 3000 to C for 4 years on simple interest at the same rate of interest and received Rs 2200 in all from both of them as interest. The rate of interest is
(1) 5%
(2) 7%
(3) 8%
(4) None of these

5. Train A and B travel to a place at a speed of 35 and 55 km/h respectively. If car B takes 7/2  hours  less time than A for the journey, the distance of the place is_
(1) 300.25 km
(2) 400 km
(3) 350.565 km
(4) 336.875 km

6.  In an exam, 60% of the total student passed. If the number of failed students is 320 then the total number of students is
(a) 600
(b) 700
(c) 800
(d) 900

7.  A cycle is bought for Rs 840 and sold at Rs 920. What is the percentage gain
(a) 10.50%
(b) 8.52%
(c) 7.35%
(d) 9.52%

8.  If Raj’s salary is 30% more than Amar’s salary, the how many percent is Amar’s salary less than that of Raj’s?
(a) 56%
(b) 23.07%
(c) 50/3%
(d) 50.6%

9. Find the number of ways in which 5 different beads can be arranged to form a necklace.
(a) 120
(b) 60
(c) 30
(d) 12

10. A card is drawn from a pack of playing cards, what is the probability of getting either a red or a red queen?
(a) 4/13
(b) 7/13
(c) 1/13
(d) 1/26

ANSWERS

1. (2)
Total students are 40 × 15 = 600
So, 18 x 16 + (12 + 14) = 456
Left student is 10 and their average is =600-456= 144÷ 10=14.4

2. (1)
The interest in 2 years is 594.5 which is 10.25% of 5800. Hence the rate of interest is 5% p.a.

3. (2)
Upstream speed = 5 km/hr
Downstream speed = 15 km/hr
Speed of boat in still water = (5 + 15)/2 = 10 km/hr
Required time = 90/10 = 9 hrs

4. (4)
Let the rate of interest is=x
(X * 5000 * 2)/100 + (3000 * 4 * x)/100 = 2200
x = 10%

5. (4)
Let Car A takes t hrs to reach  the place
Distance is same,
35 t = 55(t – 7/2)
T = 77/8
Distance = 35 * 77/8 = 336.87 km

6. (c)
Let the number of student is x out of that 40% have failed.
40/100 * x = 320
x = 320 * 100/40 = 800

7. (d)
CP = Rs 840 and SP = Rs 920
Gain = 920 – 840 = Rs 80
gain percentage = 80/840 * 100 = 9.52%

8. (b);
Amar’s salary is less than of Raj 2y
(R/100 + R * 100)% = (30/(100 + 30) * 100)%
(30/130 *100 )% = 300/13% = 23% APPROX

9. (d)
According to formula:
Number of arrangements = (5-1)!/2 = 12

10. (b)
26/52 + 2/52 = 28/52 = 7/13