Volume of block=(8 x 12 x 20) cu.cm = 1920 cu.cm
Side of largest cube = H.C.F of 8,12,20 = 4 cm
Volume of a cube=(4 x 4 x 4)=64 cu.cm
Number of cubes=(1920/64)=30
Correct Option 8)
If Anil does 40% of certain work and Sunil the remaining, it takes 41 days to complete the work but when Sunil does 65% of the same work and Anil the remaining, it takes 41½ days to finish the work. Anil is more efficient than Sunil by
Working individually, let Anil and Sunil takes x and y days respectively.
Then Anil's 1 day work=1/x and Sunil's 1 day work=1/y
As per given conditions: (40/100) / (1/x) + (60/100) / (1/y) = 41
⇒ 2x + 3y = 205 ---(i)
And (65/100) / (1/y) + (35/100) / (1/x) = 83/2
⇒ 7x + 13y = 830 ---(ii)
Solving Eqn (i) & (ii), we get x=35, y=45
Efficiency of work of Anil and Sunil = 1/35 : 1/45 = 9 : 7
.'. % Anil is more efficient than Sunil = [(9-7)/7]*100 = 28.57%
Correct Option 8)
A shopkeeper list a product at 25% above the cost price. If he offers two successive discounts of 16% and 8%, he loose Rs. 51 in this transaction. When he sells the same product at a straight discount of 24%, there is
OPtion
1) 7.5% Loss
2) 10% Gain
3) 5% Gain
4) 12% Loss
5) 7.5% Gain
6) 6.25% Loss
7) 2.5% Gain
8) 5% loss
9) 10% Loss
10) None of these
Solution
Let CP=Rs. x, then list price=Rs. 1.25x
SP after successive discounts of 16% and 8% = 1.25x*0.84*0.92 = 0.966x
Loss = CP - SP = x - 0.966x = 44
0.034x = 51
x = 1500
.'. List Price=1.25*1500=1830
SP after single discount of 24% = 1830*0.76 = 1425
Loss = 1500 - 1425 = 75
Percentage Loss = (75/1500)*100 = 5%
A boatman rows upstream from point X after 28 seconds he rows back towards point X and in 28 seconds he reaches at point Y. If distance between X and Y is 784 meters, find speed of current?
OPtion
1) 10 m/s
2) 14 m/s
3) 12 m/s
4) 18 m/s
5) 21 m/s
6) 8 m/s
7) 6 m/s
8) 9 m/s
9) 7 m/s
10) None of these
Solution
X -------- (28 sec) Upstream ----------
Y -----------(784 m)----------- X
-------------------------------(28 sec) Downstream --------------------
Let speed of the boat in still water=a m/s and speed of stream=b m/s
Distance covered in downstream in 28 sec - Distance covered in upstream in 28 sec = 784 meters
⇒ (a+b)*28 - (a-b)*28 = 784
28a + 28b - 28a + 28b = 784
56b = 784
b = 14 m/s
Correct Option 2)
5a - 3b + 4c = 344
As we require value of c, therefore expressing a and b in terms of c in above equation.
Given, a/b=9/7, b/c=5/8 ⇒ a : b : c = (9x5) : (7x5) : (8x7) = 45 : 35 : 56
.'. a/c=45/56 ⇒ a=45c/56 and b=5c/8
5a –3b + 4c = 5x(45c/56) - 3x(5c/8) + 4c = 344
Solving, we get c=56
Correct Option 5)
A sum increases by 48% in 6 years at certain rate of simple interest per annum, then how much years are required to approximately double the amount at the same annual rate of compound interest ?
Let rate=R% and principal amount=P, then with simple interest amount after 6 years = P + (PxRx6/100) = 1.48P
⇒ R=8%
With coumpound interest sum after 'n' years = P[1 + 8/100]^n = 2P
(27/25)^n = 2
⇒ n=9
Correct Option 6)
If PQR is a triangle such that PQ=15 cm, PR=15 cm, QR=18 cm, then altitude to side PR will be
OPtion
1) 29 cm
2) 15 cm
3) 14.5 cm
4) 25.4 cm
5) 21.6 cm
6) 20.4 cm
7) 14.4 cm
8) 12.5 cm
9) Cann't be determined
10) None of these
Solution
As two sides PQ, PR are same, it is an isosceles triangle, so altitude to QR will also be perpendicular bisector of QR.
Let PS be the bisector of QR, then QS=SR=9 cm.
By Pythagoras theorem, PS² + SR² = PR²
PS² = 15² - 9² = 144
PS = 12
Now, Area of the triangle = (1/2)* base*height = (1/2)*QR*PS = (1/2)*18*12 = 108 cm²
As we have to find the altitude to PR, Area=(1/2)*PR*(Altitude to PR, say h)
108 = (1/2)*15*h
h = 14.4 cm
Correct Option 7)
A man bought a chair and a table. If he sold the chair at 10 % loss and the table at 7.5 % gain, he would not lose anything; but if he sold the table at 5% loss and the chair at 5% gain, he would lose Rs. 15 in the bargain. The total cost price of a chair and a table is
Let CP of a chair=C and a table=T
0.9C + 1.075T = T+C ⇒ 3T - 4C = 0 ---(i)
0.95T + 1.05C = T+C-15 ⇒ T - C = 300 ---(ii)
Solving eqn. (i) & (ii), we get T=1200, C=900
CP of a table and a chair = 1200+900 = 2100 Rs.
Correct Option 4)
B alone can complete the work in 45 days. A is 35% more efficient than B. If A and B together started the work but after 18 days A and B left. Then C alone completed the remaining work in 3 days. If they get Rs. 9750 as wages for the whole work, then share of C in wages is
B's 1 day work = 1/45
A's 1 day work = (135/100)*(1/45) = 3/100
18 days work of A & B = 18*(1/45 + 3/100) = 47/50
Remaining work = 1 - 47/50 = 3/50
As C takes 3 days to complete the remaining work .'. C's 1 day work = (3/50)/3 = 1/50
Ratio of efficiencies of A, B & C respectively = 3/100 : 1/45 : 1/50 = 27 : 20 : 18
Ratio of share of A, B & C respectively = 27*18 : 20*18 : 18*3 = 162 : 120 : 18
C's share in total wages of Rs. 9750 = [18/(162+120+18)]*9750 = 585 Rs.
Correct Option 10) None of these