Quant Quiz-IV

1. A man can row 18 km. upstream and 36 km downstream in 9 hours. Also he can row 15 km upstream and 60 km. downstream in 10 hours. What is the rate of current ?

(a)    3 km/hr

(b)   4.5 km/hr

(c)    5 km/hr

(d)   6  km/hr

(e)   7.5 km/hr

2. If 6 men and 15 women can earn Rs. 7350 in 7 days and 10 men and 5 women can earn Rs. 10450 in 11 days. In what time 8 men and 8 women can earn Rs. 19320 ?

(a)     15 days

(b)    16 days

(c)    18 days

(d)     20 days

(e)   None of these

3. The width of a rectangle is 65% of its length. If the area of the rectangle is 2340 sq. metre then what is the difference between the length and width of the rectangle ?

(a)    18 meter

(b)   21 meter

(c)    24 meter

(d)   32 meter

(e)  39 meter

4. The breadth of a room is 3/8 times its length. The cost of carpeting it at Rs. 13.5 per sq. metre is Rs. 15876 and the cost of painting the four walls at Rs. 5 per square metre is Rs. 6160. What is the height of the room ?

(a)    5 meter

(b)   6 meter

(c)    7 meter

(d)   8 meter

(e)   9 meter

5. A rectangular tank is 24 metres long and 11 metres deep. If 1260 cu. metre of water be drawn from the tank, the level of the water goes down by 3 metres. How many cubic metres of water the tank can hold ?

(a)    4050 cu. m

(b)   4180 cu. m

(c)    4260 cu. m

(d)   4480 cu. m

(e)   4620 cu. m

6. What is the total number of solid sphere, each of diameter 9 cm, which could be moulded to form a solid metal cylinder of height 94.5 cm. and diameter 6 cm ?

(a)    4

(b)   5

(c)    6

(d)   7

(e)   8

7.  Two pipes P1 and P2 can fill a tank in 24 minutes and 30 minutes respectively. If both the pipes are opened simultaneously, after how much time should P2 be closed so that the tank is full in 20 minutes ?

(a)    4 min.

(b)   5 min.

(c)    6 min.

(d)   7 min.

(e)   8 min.

8. Mohan takes 8 days less than the time taken by Ravi to finish a piece of work. If both Mohan and Ravi together can finish it in 7.5 days, then how many days Ravi will take to finish the work alone ?

(a)    3 days

(b)   18 days

(c)    20 days

(d)   24 days

(e)   20 days or 3 days

9. A shopkeeper bought a bat and sold it at a loss of 15 %. If he had bought it for 20 % less and sold it for Rs.147.2 more, he would have had profit of 35 %. What is the cost price of bat ?

(a)    Rs. 540

(b)   Rs. 600

(c)    Rs. 625

(d)   Rs. 640

(e)   Rs. 720

10. Two equal amounts are deposited in two bank at same interest rate 12% p.a. for 7 years and 4.5 years respectively. If the different between the interest is Rs. 585 then what was each amount ?

(a)    1650

(b)   1750

(c)    1850

(d)   1950

(e)   2050

11. An amount of money grows up to Rs. 3136000 in 2 years, and up to Rs. 3512320 in 3 years, on compound interest. What is the rate of interest per annum ?

(a)    5%

(b)   8%

(c)    10%

(d)   12%

(e)   15%

1.  (b) 4.5 km/hr

Let the upstream rate be x km/hr and downstream rate be y km/hr.

And let 1/x = u and 1/y = v

18/x + 36/y = 9

== > 2u + 4v = 1…… (i)

Again, 15/x + 60/y = 10

== > 3/x + 12/y = 2

== > 3u + 12v = 2….. (ii)

Solving (i) and (ii), we get u = 1/3 and v= 1/12

== > x= 3, y= 12

Rate of current = (12-3)/2 = 9/2 = 4.5km/hr

2. Let the daily earning of a Man and Women be X and Y respectively.

Now, 6X + 15Y = 7350/7 = 1050

== > 2X+5Y = 350….(i)

Also, 10X + 5Y = 10450/11 = 950

== > 2X+ Y = 190….. (ii)

Solving (i) and (ii) we get X= 75 and Y = 40

Daily earning of 8 men and 8 women = 75x8 + 40x8 = 920

No of days = 19320/920 = 21

3. (b) 21 meter

Let the length be ‘x’ therefore width = 65x/100= 13x/20

Hence, x*13x/20 = 2340

== > x^2= 180x20 = 3600== > x= 60 = length

Difference = 35% of 60 = 35x60/100 = 21m

4. (d) 8 meter

Let the length of the room be x , so, breadth = 3x/8

Area = 3x^2/8 = 15876/13.5 = 1176

Therefore, x^2 = 3136== > x= 56= length

Breadth = 3x/8 = 21 m

Area of four walls = 6160/5 = 2h(l+b)

Area of four walla = 1232 = 2h(56+21)= 2hx77

Therefore, h = 1232/2x77 = 8 metre.

5. (e) 4620 cu. m

Let the breadth of tank be x

Volume of water = 24*x*3 = 1260 == > x= 17.5 m

Volume of tank = 24*17.5*11 = 4620 cu. m

6. (d) 7

Volume of sphere = 4πr^3/3 = 4π(4.5)^3/3 = 121.5π

Volume of cylinder = πr^2h = πx9x94.5

No. of sphere = 9x94.5xπ/ (121.5xπ) = 7

7. (b) 5 min

Let the total work be 120

Now, Efficiency of P1 = 120/24 =5

Efficiency of P2 = 120/30 =4

Efficiency of A+B together = 5+4= 9/min

Now, Let P2 be closed after X min.

If P2 would nt have closed , it would have done (20-X)mins more work

Extra Work = 4(20-X)

Suppose P2 nt closed then extra work will be added to the total wrk so as to take a total of 20 min

Now, Total work = 120+4(20-X)

Time = 20

Efficiency together =9

20x9 = 120+4(20-X)

4x = 200-180 = 20

X= 5min

Hence, P2 was closed after 5 mins.

8.  (c) 20 days

Let Ravi takes x days, mohan will take (x-8) days

Now, Suppose total work be x(x-8)

Efficiency of Ravi = x-8

Efficiency of Mohan = x

Efficiency of Ravi+mohan = 2x-8

Time = 7.5 days

Work = x(x-8)

Therefore, x(x-8)/ 2x-8 = 7.5

== > x(x-8) = 15x-60

== > x^2-23x+60 = 0

Solving , we get x= 3 or 20

3 will be neglected as this implied that mohan will do it in -5 days, which is practically nt possible.

9. (d) Rs. 640

Let CP be X, then SP = 85X/100 = 17X/20

If Case,

CP = 80X/100 = 4X/5

SP = (17X/20) + 147.20

Profit = 35%

SP = 135x4X/500

SP = (17X/20) + 147.20

Therefore, Comparing both we get,

27X/25 = (17X+2944)/20

540X-425X = 25x2944

115X= 25x2944

X= 25x2944/115 = 5x128 = 640

10. (d) 1950

Acc to question Sum ,P is same R= 12% in both case

Then Interest of Rs.585 will be the interest of the difference of time period= (7-4.5)= 2.5 years

Now, P = 100xSI/RT = 100x585/12x2.5

P = 100x585//30 = 1950

11. (d) 12%

Compound Interest for 3rd year = 3512320-3136000 = 376320 which is SI for 1 year on Rs.3136000.

R= 100xSI/PT = 100x376320/3136000

R = 12%