1)A number being successively divided by 3, 5 and 8 leaves 1,2 and 4 as remainders respectively. What are the remainders if the order of divisors be reversed?
(a) 3, 3, 1 (b) 3, 1, 3
(c) 1, 3, 3 (d) None of these
Explanation :-
Complete remainder = d1d2r3+d1r2+r1
= 3 × 5 ×4 + 3 × 2 + 1 = 67
Divided 67 by 8, 5 and 3, the remainders are 3, 3, 1. Ans:(a)
2) 4 goats or 6 sheeps can graze a field in 50 days. 2 goats and 9 sheeps can graze the field in
(a) 100 days (b) 75 days
(c) 50 days (d) 25 days
Explanation :-
Given that 1 Goats =3/2 sheeps.
Now, 2 goats + 9 sheeps
2 x 3/2 sheeps + 9 sheeps
= 12 sheeps
Here M1D1 = M2 D2
Þ 6´50 = 12´d2
d2 = 25 days Ans:(d)
3) A contractor undertakes to built a walls in 50 days. He employs 50 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
(a) 25 (b) 30 (c)35 (d) 50
Explanation :-
50 men complete 0.4 work in 25 days.
Applying the work rule,
m1´d1´w2 = m2´d2´w1
we have,
50´25´0.6 = m2 ´25´0.4
or m2 = 75men
Number of additional men required
= (75 – 50) = 25
Ans : (a)
4) What least number must be subtracted from 1936 so that the remainder when divided by 9, 10, 15 will leave in each case the same remainder 7?
(a) 29 (b) 39 (c) 49 (d) 59
Explanation :-
The LCM of 9, 10 and 15 = 90
On dividing 1936 by 90,
the remainder = 46
But 7 is also a part of this remainder.
the required number = 46-7 = 39
Ans: (b)
5) 24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is :
(a) 30 (b) 32 (c) 34 (d) 36
Explanation :-
m1´d1´t1´w2 = m2´d2´t2´w1
24×10×8×1 = m2×6×10×1
m2 = 32men Ans : (b)
6) R and S start walking each other at 10 AM at the speeds of 3 km/h and 4 km/h respectively. They were initially 17.5 km apart. At what time do they meet?
(a) 2 : 30 PM (b) 11 : 30 AM
(c) 1 : 30 PM (d) 12 : 30 PM
Explanation :-
Let after t hours they meet then,
3t + 4t = 17.5 Þ t = 2.5
Time = 10 am + 2.5 h = 12 : 30pm
Ans : (d)
7) If sin (x + y) = cos [3(x + y)], then the value of tan [2(x + y)] is
(a) 1 (b) 0 (c) 2 (d)3
Explanation :-
sin (x + y) = cos [3(x + y)]
cos [90° – (x + y)] = cos [3(x + y)]
90° – (x + y) = 3(x + y)
4(x + y) = 90°
2(x + y) = 45°
tan [2(x + y)] = tan 45° = 1
Ans:(a)
8) A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the alt itude of the parallelogram is 100 m, then the altitude of the triangle is :
(a) 100 m (b) 200 m
(c) 141.4m (d) 14.14 m
Explanation :-
Let the common base be x m.
Now, area of the triangle = area of the parallelogram
1/2 x Altitude of the triangle = x × 100
Altitude of the triangle = 200 m
Ans :(b)
9)In a 800 m race around a stadium having the circumference of 200 m, the top runner meets the last runner on the 5th minute of the race. If the top runner runs at twice the speed of the last runner, what is the time taken by the top runner to finish the race ?
(a) 20 min (b) 15 min
(c) 10 min (d) 5 min
Explanation :-
After 5 minutes (before meeting), the top runner covers 2 rounds i.e., 400 m and the last runner covers 1 round i.e., 200 m. Top runner covers 800 m race in 10 minutes.
Ans : (c)
10)The sum of five numbers is 290. The average of the first two numbers is 48.5 and the average of last two numbers is 53.5. What is the third number?
(a) 72 (b) 84 (c) 96 (d) 86
Explanation :-
Third number = 290–2×48.5–2×53.5
= 290 – 97 – 107 = 86 Ans : (d)
11)What greatest number can be subtracted from 10,000 so that the remainder may be divisible by 32, 36, 48 and 54 ?
(a) 9136 (b) 9191
(c) 9933 (d) 9216
Explanation :-
LCM of 32, 36, 48, 54 = 864 Ans : (a)
12)The average marks in Science subject of a class of 20 students is 68. If the marks of two students were misread as 48 and 65 of the actual marks 72 and 61 respectively, then what would be the correct average ?
(a) 68.5 (b) 69 (c) 69.5 (d) 70
Explanation :-
Difference of marks
= 72+61–48–65= 20
Correct average marks
=68+ 20/20=68+1= 69
Ans:(b)
13) What is the ratio between the total values of quantity sold for items E and F respectively? .
(a) 15 : 14 (b) 3 : 2
(c) 5 : 7 (d) 7 : 5
Explanation :-
Required ratio = 15 × 25 : 10 × 35
= 3 × 5 : 2 × 7 = 15 : 14
Ans:(a)
14)A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmphThis train catches up the goods train in 4 hours. Find the speed of the goods train.
(a) 36 kmph (b) 40 kmph
(c) 30 kmph (d) 42 kmph
Explanation :-
Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours
= Distance covered by express train in 4 hours.
10x = 4×90 or x = 36.
So, speed of goods train = 36 kmph
Ans:(a)
15)A and B can finish a work in 10 days while B and C can do it in 18 days. A started the work, worked for 5 days, then B worked for 10 days and the remaining work was finished by C in 15 days. In how many days could C alone have finished the whole work?
(a) 30 days (b) 15 days
(c) 45 days (d) 24 days
Explanation :-
Let C completes the work in x days.
Work done by (A+B) in 1 day =1/10
Work done by (B+C) in 1 day =1/18
A’s 5 days’ work + B’s 10 days’ work + C’s 15 days’ work = 1
or (A + B)’s 5 days’ work + (B + C)’s 5 days’ work + C’s 10 days’ work = 1
or 5/10 + 5/18 + 10/x = 1
x = 45 days Ans:(c)
- Mr. K. Kumar
Senior Faculty
Hyderabad
ph:9492956214