A, B, C and D are four positive numbers such that A is 2/3 times of B, B is 5/6 times of C and C is 3/5 times of D. If the average of 3 times of A and 4 times of D is 900, then the average of all four numbers A, B, C and D is:
A=(2/3)*(5/6)*(3/5)*D
D=3A
Also, average of 3 times A and 4 times D = 900
⇒ 3A + 4D = 1800
Now substituting D=3A in above equation, we get, D + 4D = 1800
D=360
.'. A=360/3=120
B=(3/2)*A=(3/2)*120=180
C=(3/5)*D=(3/5)*360=216
Hence, average of A, B, C & D = (120+180+216+360)/4 = 876/4 = 219
Correct Option 8)
A dishonest shopkeeper professes to sell at a discount of 15% to his cost price but uses 400 gm instead of 500 gm. The actual gain or loss percentage is
OPtion
1) 5.33% Loss
2) 6.75% Gain
3) 6.66% Gain
4) 6.25% Gain
5) 7.66% Loss
6) 7.33% Gain
7) 4.84% Gain
8) 3.33% loss
9) 4.25% Gain
10) None of these
Solution
For shopkeeper, let CP of 1 kg or 1000 gm = 100
As he is using 400 gm instead of 500 gm .'. For 1 kg price, he actually sells 800 gm
CP of 800 gm = 80
With 15% discount, SP of 800 gm = (100-15) = 85
.'. % Gain = [(85-80)/80]*100 = 25/4 or 6.25%
Correct Option 4)
Let 7A=4B=8C=k then A=k/7, B=k/4, C=k/8.
A : B : C = k/7 : k/4 : k/8
Multiply the ratio by 56 (LCM of 7,4,8)
A : B : C = 8k : 14k : 7k
The minimum possible values of A, B & C are for k=1
.'. A=8, B=14, C=7 and minimum sum=8+14+7=29
When letters from A to Z are numbered from 1 to 26 respectively, the coding of letters is 3 letters forward and 2 letters backward positions alternatively.
F O R G I V E = (F+3), (O-2), (R+3), (G-2), (I+3), (V-2), (E+3) = I M U E L T H
P U R P O S E = (P+3), (U-2), (R+3), (P-2), (O+3), (S-2), (E+3) = S S U N R Q H
M U N D A N E = (M+3), (U-2), (N+3), (D-2), (A+3), (N-2), (E+3) = P S Q B D L H
Correct Option 7)
Given equation: 10x² + kx + 6 = 0
The roots are in the ratio 3:4. Let roots of the equation are 3ɑ and 4ɑ.
Applying condition for sum and product of the roots,
Sum of roots = 3ɑ + 4ɑ = -k/10 ---(i) and
Product of roots = 3ɑ*4ɑ = 6/10 = 3/5
12ɑ² = 3/5
ɑ = ±1/(2√5)
From (i), k = -70ɑ
.'. k = -70*(-1/(2√5)) = 7√5
Three cylinders of height of 8 cm and diameters 0.24 m, 0.28 m and 0.16 m respectively are melted to form spherical solid balls of diameter 4 cm, then number of balls thus formed is
Nine men can finish a work in 20 days whereas 12 women can finish the same work in 18 days. If six men and nine women started working together. After 8 days 3 women left and 2 new men joined the work, The group continued working together till the end of the work. In how many days will they be able to do the remaining work ?
9 men can finish work in 20 days, so 1 man's 1 day work=1/(9x20)=1/180
12 women can finish work in 18 days, so 1 woman's 1 day work=1/(12x18)=1/216
6 men & 9 women's 8 days work=8x(6/180 + 9/216)=3/5
Remaining work=1 - 3/5=2/5
Given, after 8 days 3 women left and 2 new men joined, so in new group there are 8 men and 6 women
Now 8 men + 6 women's 1 day work=8*(1/180) + 6*(1/216) = 13/180
.'. Time required to complete remaining work = (2/5)/(13/180) = 72/13 days
Correct Option 5)
A pipe can fill a tank in 8 hours. After 3/5 of the tank is filled, four more pipes of half capacity are opened to fill the tank. What is the total time taken to completely fill the tank ?
Time taken by first pipe to fill the tank = 8 hours
.'. Time taken by first pipe to fill 3/5 of the tank = (3/5)/(1/8) = 24/5 hours
Remaining part of the tank to be filled = 1 - 3/5 = 2/5
Part of the tank filled by 1 existing pipe and 4 new pipes in 1 hour = 1/8 + 4x(1/16) = 3/8
Time taken by 5 pipes to fill remaining tank = (2/5)/(3/8) = 16/15 hours
.'. Total time taken = 24/5 + 16/15 = 88/15 hours = 5 hours 52 minutes.
Correct Option 6)
The average of some numbers is 57. If 68% of the numbers are increased by 6 and the remaining are decreased by 8, then the average so obtained will be:
Let there be total 'x' numbers, then new average = (57x + 0.68x*6 - 0.32x*8) / x = 58.52
Alternate Method:
Let there be 100 numbers and their average is 57, Sum=5700
For 68 numbers average=(57+6)=63, Sum=68*63=4284
For remaining 32 numbers average=(57-8)=49, Sum=32*49=1568
New average = (4284+1568)/100 = 58.52
Correct Option 5)
MATHEMATICS IS NOT CRAMMING OR LEARNING ITS JUST LOGIC OR CREATIVITY..............
PANKAJ AGGARWAL
"The gaming of numbers is called maths.So participate in this wonderful game and explore in it,learn in it and enjoy in it.Then only you can pass in this wonderful game."