Q1.
If a number is as much greater than 31 as it is less than 75, then the number is.
(a)106 (b)44 (c)74 (d) 53
Solution.
If the number be x , then
x - 31 = 75 - x
= 2x = 75 + 31 = 106
x = 53
Solution
Q2.
The LCM of two numbers is 520 and their HCF is 4.If one of the number is 52, then the other number is.
(a)40 (b)42 (c)50 (d) 52
Solution.
First number x second number= HCF x LCM
52 x second number= 4 x 520
second number = (4 x 520)/52 = 40
Solution
Q3.
(0.9 x 0.9 x 0.9 + 0.1 x 0.1 x 0.1) is equal to.
(a)0.73 (b)0.82 (c)0.91 (d)1.00
Solution.
(0.9)3 + (0.1)3
= 0.729 + 0.001
=0.73
Solution
Q4.
The value of 0.65 x 0.65 + 0.35 x 0.35 + 0.70 x 0.65 is.
(a)1.75 (b)1.00 (c)1.65 (d)1.55
Solution.
Expression = 0.65 x 0.65 + 0.35 x 0.35 + 2 x 0.35 x 0.65
=(0.65 + 0.35)2
= (1)2=1
{a2+b2+2ab = (a + b)2}
Solution
Q5.
12kg of rice costing Rs. 30 per kg is mixed with 8 kg of rice costing Rs 40 per kg. The average per kg price of mixed rice is.
(a)Rs 38 (b)Rs37 (c)Rs35 (d)Rs34
Solution.
Total cost price of 20kg of mixed rice
Rs(12 x 30 + 8 x 40)
= Rs680
Average per kg price
680/20 = Rs34
Solution
Q6.
If b is the mean proportional of a and c, then (a - b)3:(b - c)3 equals..
(a)a3:c3 (b)b2:c2 (c)a2:c2 (d)a3:b3
Solution.
Since b is the mean proportional a and c.
a/b = b/c = k (suppose)
a = bk , b = ck
(a - b)3/(b - c)
3 = (bk - b)3/(ck - c)3
b3(k - 1)3/c3(k - 1)3
b3/c3 = a3/b3
Solution
Q7.
A team played 40 games in a season and won in 24 of them. What percent of games played did the team win
.
(a)70% (b)40% (c)60% (d) 53%
Solution.
Required percentage
24/40 x 100 = 60%
Solution
Q8.
By selling an article for Rs960 a man incurs a loss of 4% what was the cost price?
(a)Rs1,000 (b)Rs784 (c)Rs498.4 (d) Rs300
Solution.
C.P of article
= 100/(100 - loss percent) x S.P
= 100/96 x 960 = Rs1,000
Solution
Q9.
THe diference between a single discount of 30% on Rs550 and two successive discounts of 20% and 10% on the same amount is.
(a)Nil (b)Rs11 (c)Rs22 (d) Rs44
Solution.
Case I. A single discount is 30%
Case II. Two successive discounts of 20% and 10%
Single equivalent discount
(20 + 10 - 20 x 10/100)% = 28%
Difference = (30 - 28)% = 2%
Required difference
= 2% of 550
Rs 2 x 550/100 = Rs11
Solution
Q10.
A sum of money amounts to Rs850 in 3 years and to Rs925 in 4 years at same rate of simple interest.The sum is .
(a)Rs550 (b)Rs600 (c)Rs625 (d) Rs700
Solution.
Interest for 1 year = Rs (925 - 850) = Rs 75
If a sum becomes a1 in t1 years a2
in t 2 years then rate of
interest = 100(a2- a1)/(a1t2 - a2
t1)%
= 100(925 - 850)/(850 x 4 - 3 x 925)
= 7500/625 = 12%
Principal = SI x 100/Time x Rate
75 x 100/1 x 12 = Rs 625
Solution
Q11.
A and B together can complete a piece of work in 72 days.B and C together can complete it in 120 days and A and C together in 90 days.
In what time can A alone complete the work?
(a)80 days (b)100 days (c)120 days (d)150 days
Solution.
A alone can do in
(2 x 72 x 120 x 90)/(72 x 120 + 120 x 90) = 6480
144 x 10800/12960 = 120 days
Solution
Q12.
Two pipes A and B are fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together the time taken to fill
the tank is.
(a)50 minutes (b)12 minutes (c)25 minutes (d)15 minutes
Solution.
Part of the tank filled by both pipes in one minute.
= 1/20 + 1/30
Required time = 1/(1/20 + 1/30)
20 x 30/50 = 12 minutes
Solution
Q13.
The speed of a bus in 72km/hr. The distance covered by the bus in 5 seconds ie .
(a)100m (b)60m (c)50m (d)654m
Solution.
Speed of bus = 72km/hr
= (72 x 5/18)metre/second
20 metre/second
Required distance
20 x 5 = 100 metre
Solution
Q14.
The speed of a boat in stil water is 10km/hr. It covers (upstream)a distance of 45km in 6 hrs. The speed(in km/hr) of the stream is.
(a)2.5 (b)3 (c)3.5 (d)4
Solution.
Upstream speed of boat
=Distance/Time = 45/6 = 15/2
= 7.5 km/hr
Speed of current = 10 - 7.5
= 2.5 kmph
Solution
Q15.
If (a - 1)2 + (b + 2)2 + (c + 1)2 = 0, Then the value of 2a - 3b + 7c is.
(a)12 (b)3 (c)11 (d)1
Solution.
(a - 1)2 + (b + 2)2 + (c + 1)2 = 0
a - 1 = 0, a = 1
b + 2 = 0, b = -2
c + 1 = 0,
c = -1
2a -3b + 7c
2 - 3(-2)+ 7(-1)
2 + 6 - 7 = 1
Solution
