A father is 30 times older than his son. 18 years later, he will be only thrice as old as his son. Father's present age in years is
F = 30 S
or, S = F/ 30
Also, F + 18 = 3(S + 18)
∴ F + 18 = 3( F/ 30 + 18)
or, F + 18 = F /10 + 54
or, F  F /10 = 36 or, 9 /10 F = 36
or, F = 36 x 10 /9 = 40 yrs
Rajneetha walks around the circular park in 15 minutes. If she walks at the rate of 5 km/hr, how much distance would she have to travel, at the minimum, to reach the centre of the park from any point on its perimeter?
Time = 15 minutes
= 15 x 60 sec = 900 sec
Speed = 5 km/hr
= 5 x 5/ 18 m/sec
= 25 18 m/sec
Now Perimeter of the circular park = D
= S x T
= 25/ 18 x 900
2πR = 1250 metre
R = 1250 x 7 /2x 22 = 8750/ 44
= 198.86 metres
∴ Required minimum distance to reach the centre of the circle = 200 metre (approx)
The ratio of the number of boys and girls in a school is 3:2. 10% of the boys and 25% of the girls are scholarship holders. The percentage of the school students who are not scholarship holder is
Let the boys = 3x
girls = 2x
An anti aircraft gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy aircraft will bring the aircraft down?
The enemy aircraft will be brought down even if one of the four shots hits the aircraft.
The opposite of this situation is that none of the four shots hit the aircraft.
The probability that none of the four shots hit the aircraft is given by:
(1 − 0.7)(1 − 0.6)(1 − 0.5)(1 − 0.4) = 0.3 x 0.4 x 0.5 x 0.6 = 0.036
So, the probability that at least one of the four hits the aircraft:
= 1 – 0.036 = 0.964
If a:b=c:d=e:f=1:2, then (pa+qc+re):(pb+qd+rf) is equal to
a : b = c : d = e : f = 1 : 2 = k
a = k, b = 2k, c = k, d = 2k, e = k, f = 2k
pa + qc + re = pk + qk + rk
= k (p + q + r)
pb + qd + rf = p x 2k + qx 2k + r x 2k
= 2k(p + q + r)
∴ (pa + qc + re) : (pb + qd + rf)
= k(p + q + r) : 2k(p + q + r)
= 1: 2
Mr. Anuraag Awasthi deposits an amount of Rs 56500 to obtain a simple interest at the rate of 12 p.c.p.a. for 3 years. What total amout will Mr. Anurrag Awasthi get at the end of 3 years ?
SI = P x R x T 100
⇒ SI = 56500 x 12 x 3 100
⇒ SI = Rs 20,340
⇒ Amount = Principle + SI
⇒ Amount = Rs (56500 + 20340) = Rs 76840
How many metres of cloth 1.1m wide will be required to make a conical tent whose vertical height is 12m and base radius is 16m?
Radius of cone, r = 16m
Height of cone, h = 12m
Slant height of cone = l = h 2 + r 2
= 12 2 + 16 2 = 144 + 256 = 400 = 20 m
Area of cloth required = Lateral surface area of the cone = πrl
= 22 7 x 16 x 20 = 7040 7 sq.m
Width of the cloth = 1.1m
∴ Length of the cloth = Area Width = 7040 x 10 7 x11 = 6400 7 = 914 2 7 metres
In each of the following questions, two equations are given. You have to solve these equations and
2. I. x^{2}  24x + 144 = 0
II. y^{2}  26y + 169 = 0
I. x^{2}  24x + 144 = 0
⇒ x^{2}  12x  12x + 144 = 0
⇒ x(x  12)  12 (x  12) = 0
⇒ (x  12) (x  12) = 0
⇒ x = 12
II. y^{2}  26y + 169 = 0
⇒ (y  13)^{2} = 0
⇒ y  13 = 0
⇒ y = 13
x < y
In each of the following questions, two equations are given. You have to solve these equations and
I. 2x^{2} + 3x  20 = 0
II. 2y^{2} + 19y + 44 = 0
I. 2x^{2} + 3x  20 = 0
⇒ 2x^{2} + 8x  5x  20 = 0
⇒ 2x (x + 4)  5 (x + 4) = 0
⇒ (x + 4) (2x  5) = 0
⇒ x = 4 or 5252
II. 2y^{2} + 19y + 44 = 0
⇒ 2y^{2} + 11y + 8y + 44 = 0
⇒ y(2y + 11) + 4 (2y + 11) = 0
⇒ (y + 4) (2y + 11) = 0
⇒ y = 4 or 112112
x ≥ y
These questions are based on the graph which shows the Demand and Production statistics of the five companies.
What is the ratio of companies having more demand than production to those having more production than demand?
A, C and E have more demand.
B and D have more production .
So the ratio is 3 : 2
These questions are based on the graph which shows the Demand and Production statistics of the five companies.
What is the difference between the average demand and the average production of five companies taken together ?
Avg Demand = (3000 +600+2500+1200+3300)/5=10600/5 = 2120
Avg Production = 1840
So the Diff is 280
Percentage distribution of candidates studying in various disciplines of a college and the percentage of girls in each discipline.
Percentage break up of student in each discipline
What is the number of girls studying in Engineering discipline ?
Total number of girls studying in Engineering discipline
= 12% of total number of girls
= 2000 � 12/100 = 240
Percentage distribution of candidates studying in various disciplines of a college and the percentage of girls in each discipline.
Percentage break up of student in each discipline
Which discipline has the highest number of boys studying in it ?
Number of boys in Science discipline
= 4800 � 37/100  2000 � 32/100
= 1776  640 = 1136
Number of boys in Commerce discipline
= 4800 � 21/100  2000 � 24/100
= 1008  480 = 528
Number of boys in Arts discipline
= 4800 � 18/100  2000 � 14/100
= 864  280 = 584
Number of boys in Management discipline
= 4800 � 10/100  2000 � 8/100
= 480  160 = 320
Hence, highest number of boys are studying in Science discipline.
The following table gives the tariff [in paise per kilowatthour (k Wh)] levied by the UPSEB in 199495, in four sectors and the regions within them. The table also gives the percentage change in the tariff as compared to 199192.
The UPSEB supplies power under four categories; urban (25%), domestic (20%), industrial (40%), and rural (15%). In 199495, the total power produced by the UPSEB was 7875 megawatts.
If in 199495, there was a 10% decrease in the domestic consumption of powers as compared to that in 199192, what was the consumption of power in the rural sector in 199192?
The domestic consumption in 199192 = 1,575/0.9 = 1,750 megawatts.
This constitutes 20% of total power consumed in 9192 and the rural consumption constitutes 15% of total power in 9192
Hence in 199192, the rural consumption = (1,750 � 15201520) = 1,312 megawatts
The following table gives the tariff [in paise per kilowatthour (k Wh)] levied by the UPSEB in 199495, in four sectors and the regions within them. The table also gives the percentage change in the tariff as compared to 199192.
The UPSEB supplies power under four categories; urban (25%), domestic (20%), industrial (40%), and rural (15%). In 199495, the total power produced by the UPSEB was 7875 megawatts.
In the given two years, what is the total tariff paid by the urban sector ?
The rates for the urban sector is not known
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