Pipes A and B are fitted to a tank. A can fill the tank in 1½ hours and capacity of B which is emptying pipe is half that of A. If B is fitted at one-third of the height of the tank from the base and both the pipes are opened simultaneously, then time taken to fill the empty tank is:
Filling capacity of A per hour = 2/3, .'. Emptying capacity of B per hour = (1/2)*(2/3) = 1/3
As B, the emptying pipe is fitted at 1/3 of the height of the tank from base, so the draining will start only after tank is 1/3 full.
Now time taken to fill 1/3 tank by A = (1/3)/(2/3) = 1/2 hrs.
Effective filling per hour after 1/3 tank is full = 2/3 - 1/3 = 1/3
.'. Time required to fill remaining 2/3 tank = (2/3) / (1/3) = 2 hrs
Total time = (1/2 + 2) Hrs = 2 hours 30 minutes
Correct Option 8)
C with his 200% efficiency, can complete 25% of certain work in 12 days. B is 20% more efficient than C. A with 75% efficiency can complete the work in same days as B. If A and B together finish the same work and A gets Rs 10400, then what is the share of B ?
With 200% efficiency C can complete 25% work in 12 days.
⇒ C with 100% efficiency can complete the work in 96 days.
B is 20% more eficient than C, so B can complete the work in 96*(100/120)=80 days.
A with 75% efficiency can complete the work in same days as B ⇒ (100/75)*A=80
.'. A can complete the work in 60 days.
Ratio of efficiencies of A and B = 1/60 : 1/80 = 4 : 3
B's share = (3/4)*10400 = 7800
Correct Option 5)
Wheat costing Rs. 42 and Rs. 36 per kg is mixed with third variety in the ratio 3:4:5. If this mixture cost Rs. 46.5 per kg, then per kg price of wheat of third variety is:
Let the quantity of 1st, 2nd and 3rd variety be 3 kg, 4 kg and 5 kg respectively, then total quantity=12 kg
Let the cost of 3rd variety be Rs x/kg, then Avg. cost of final mixture = (3*42 + 4*36 + 5*x) / 12 = 46.5
270 + 5x = 558
5x = 288
x = 57.6
Correct Option 4)
When letters from A to Z are numbered from 1 to 26 respectively, then coded number is a sequence of two-digit number obtained by adding pair of position number 1st and last, 2nd and last but 1 and so on ..
BAISAKHI (2, 1, 9, 19, 1, 11, 8, 9) = 11 09 20 20
NAVRATRI (14, 1, 22, 18, 1, 20, 18, 9) = 23 19 42 19
DIWALI (4, 9, 23, 1, 12, 9) = 13 21 24
Correct Option 5)
On this Diwali, Akash a tech guy, decorated his home by a series of LED lights of three different colours: blue, red and green where he uses total 100 LED lights and also spends exactly Rs. 100 on making this series. If cost of blue LEDs is Rs. 4 for 3, red LEDs Rs. 3 for 9 and green LEDs Rs. 7 for 10, then which of the following can be the number of blue LEDs in the series ?
B + R + G = 100 --- (i) and
B*(4/3) + R*(3/9) + G*(7/10) = 100 ⇒ 40B + 10R + 21G = 3000 ---(ii)
Multiplying eqn. (i) by 10 and subtracting it from (ii), we get 30B + 11G = 2000
B = (2000 - 11G)/30
We get the integer value of B for G=10 and 40, so that count of total lights is 100.
Therefore combinations of Blue, Red & Green are B=63, R=27, G=10 OR B=52, R=8, G=40
Correct Option 5)
Ratio of income of Jayesh to the expenditure of Suresh is 4:3 and Jayesh spends 85% of his income whereas Suresh spends 90% of his income. If savings of Suresh is Rs. 6000 less than that of Jayesh, then the income of Suresh (in Rs) is
Let income of Jayesh=4x and expenditure of Suresh=3x
Expenditure of Jayesh=85% of 4x=17x/5
Savings of Jayesh=4x - 17x/5=3x/5
Income of Suresh=(100/90)*3x=10x/3
Savings of Suresh=10x/3 - 3x=x/3
Difference of savings of Jayesh & Suresh = 3x/5 - x/3 = 6000
Solving, we get x=22500
.'. Income of Suresh=10*22500/3=75000
Correct Option 6)
A boy standing on a ground sees an angle of elevation of 30° to the top of a tower 50 m high . When he started walking towards tower in a straight line, after 3 minutes he observes an angle of elevation of a top of a tower as 60°, then walking speed of a boy is
Let distance walked by boy from starting point where he observes an angle of elevation 30° and the point where he observes angle of elevation 60° be 'x' m and the distance of base of a tower from starting point be 'y' m.
Then, trignometric ratios:
tan 30 = 50/y
1/√3=50/y ⇒ y=50√3 ---(i)
Also, tan 60 = 50/(y-x)
√3=50/(y-x) ⇒ y-x=50/√3 ---(ii)
Substituting value of y from (i) into (ii), we get x=100√3
Now, the distance travelled 'x' in 3 minutes is 100/√3 m, so distance/hr=(60/3)*100/√3=1154.7 m
Speed=1.1547 km/hr
Correct Option 7)
When there is 12.5% fall in price of a chocolate bar, a person is able to purchase 40 more in Rs. 800. The cost (in Rs) of 100 chocolate bars at reduced price is:
Let the initial price of chocolate bar =Rs. x and Number=n
Then, x*n = 800
Also, 0.875x*(n+40) = 800
⇒ 0.875x*n + 35x = 800
0.875*800 + 35x = 800
x = 20/7
Cost of 100 chocolate bar at reduced price = 100*0.875*(20/7) = 250
Correct Option 9)
In 2022, population of a city is 16 Lakh. Next year in 2023 it increases by 15% but in subsequent year 2024, it decreases by 10%. If this trend continues, then find the number of women in a city in 2027, if ratio of men, women and children after five years is 9:8:10
Total population after 5 years (from 2022 to 2027) = 1600000*(115/100)*(90/100)*(115/100)*(90/100)*(115/100) = 1971054
Given, ratio of men, women, children = 9 : 8 : 10
.'. Number of women = (8/27)*1971054 = 584016
Correct Option 6)