IPPB Mains Online Test Series 1, IPPB Mains Mock Test Series 1st

Let A worked for x days.
x/21 + 4/28 = 1 => x/21 = 6/7 => x = 18
A worked for 18 days. So, A can complete the remaining work in 18 – 4 = 14 days.

5:1 = x: 10
x = 50

Sum of 10 even numbers = 10 * 11 = 110
Average = 110/10 = 11

?/9261 = (11/21)³ = 1331/9261
=> ? = 1331

Let the sum be Rs. 100. Then,
S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5
S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25
So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 – 100) = 10.25%.

Area of a parallelogram = base * height = 24 * 16 = 384 cm²

Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x – 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.

Let C.P. be Rs. x.
Then, 5% of x = 350 – 340 = 10
x/20 = 10 => x = 200

110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500

S.I for 5 years = (1020 – 720) = Rs. 300.
S.I. for 2 years = 300/5 * 2 = Rs. 120.
Principal = (720 – 120) = Rs. 600.

109 * 34 – 108 * 33
= 3706 – 3564 = 142

DS = 6
US = 4
S = ?
S = (6 – 4)/2 = 1 kmph

Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 – 7/15 = 8/15
Part filled by B in 1 minute = 1/20
1/20 : 8/15 :: 1 ; x
x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.
The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.

D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.

Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 ——– 7
4 ——— ? → 28 m

Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec

Walk, Talk, Drink and Lick are verbs, but not Plank.

1000/71 = 14 6/71
1000 + 71 – 6 = 1065

√3/4a² = 4√3 → a = 4

Let 4207 – x = 3007
Then, x = 4207 – 3007 = 1200

SP per metre = 18000/400 = Rs. 45 Loss per metre = Rs. 5 CP per metre = 45 + 5 = Rs. 50

(A + B)’s 1 day work = 1/12;
(B + C)’s 1 day work = 1/15;
(A + C)’s 1 day work = 1/20
Adding, we get: 2(A + B + C)’s 1 day work = (1/12 + 1/15 + 1/20) = 1/5
(A + B + C)’s 1 day work = 1/10
So, A, B and C together can complete the work in 10 days.

Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.

Relative speed = (40 – 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.

70 a = 40 b
a: b = 4: 7

1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750

x ——- 9
(x + 10) —- 6
x * 9 = (x + 10)6
x = 20

Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X – 48 = 180
1000/x – 48 * 5/18 = 180
50 = 9X – 120
X = 68 Kmph

2x² + 6x – 3x – 9 = 0
2x(x + 3) – 3(x + 3) = 0
(x + 3)(2x – 3) = 0
=> x = -3 or x = 3/2.

Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.

Let the article be worth Rs. x.
C.P. 90% of Rs. x = Rs. 9x/10
S.P. = 110% of Rs. x = Rs. 11x/10
Gain = (11x/10 – 9x/10) = Rs. x/5
Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%

When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 – 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.

Let the ten’s digit be x. Then, unit’s digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) = 144
2×2 + 26x – 140 = 0
(x – 2)(11x + 35) = 0
x = 2
Hence, required number = 11x + 2 = 24.

(60/100) * 50 – (40/100) * 30
30 – 12 = 18

1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 365 = 266 * 3 = 798
=                                  ———–
=                                       987

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec = 6 sec

Let C.P. = Rs. x.
Then, S.P. = Rs. (12% of x) = Rs. 6x/5
New S.P. = 2 * 6x/5 = Rs. 12x/5
Profit = 12x/5 – x = Rs. 7x/5
Profit = 7x/5 * 1/x * 100 = 140%.

There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee = ⁶C₃ = (6 * 5 * 4)/6 = 20.

(25/100) * (30/100) * (45/100)
1/4 * 3/10 * 9/20
27/800 = 0.03375

M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4

By the time A covers 1000 m, B covers (1000 – 50) = 950 m.
By the time B covers 1000 m, C covers (1000 – 100) = 900 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.
So in 1000 m race A beats C by 1000 – 855 = 145 m.

HCF of 4956, 3894 = 354
(4956 – 3894)/354 = 3

We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e., = 500 ways.

The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000

Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x – 49x/50 = x/50
x/50 = 400 => x = 20000

Let the cost price for the manufacturer be Rs. x. Then, 125% of 120% of 118% of x = 30.09.
125/100 * 120/100 * 118/100 * x = 3009/100
177/100 x = 3009/100 => x = 17