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)