__Knowledge philic presents__

__Daily quiz- 01 sep 2015__
1. If a shopkeeper
sales a cow at 16(2/3) % profit and a buffalo at 12(1/2)% loss, he gains Rs. 30
in whole transaction. If he sales a cow at 12.5 % loss and the buffalo at
16(2/3)% profit he neither gains nor losses. Find sum of their prices ?

(a) 620

(b) 720

(c) 725

(d) 625

(e) None of these

**(b) Rs. 720**

__solution:-__
Let the price of Cow
and Buffalo be X and Y respectively.

Now, ATQ

7X/6 + 7Y/8 = X+Y+30

== > 28X + 21Y =
24X+24Y+720

== > 4X – 3Y =
720…(i)

Also, 7X/8 + 7Y/6 =
X+Y

== > -3X + 4Y = 0
…(ii)

Adding (i) and (ii),
we get

X+Y = 720

2. When a train is
running at a speed of 7/11 of its usual speed, it takes 22 hours to cover a
certain distance. Find the actual time to cover the certain distance ?

(a) 14 hours

(b) 20 hours

(c) 8 hours

(d) 12 hours

(e) None of these

**(a) 14 Hours**

__solution:-__
New Speed = 7/11 of
usual speed

New Time Taken =
11/7 of usual time.

22 = 11/7 of usual
time

Usual Time = 22*7/11
= 14 hours.

3. Three taps A, B
and C can file a tank in 12 hours, 15 hours and 20 hours respectively. First
tap opened at 7 am., 2nd tap opened at 10 am. and 3rd tap opened at 11 am. At
what time the tank will fill completely ?

(a) 3PM

(b) 2PM

(c) 6PM

(d) 1PM

(e) None of these

**. (b) 2PM**

__solution:-__
Let the total work
be 180

Efficiency of A =
180/12 = 15/hr.

Efficiency of B =
180/15 = 12/hr.

Efficiency of C =
180/20 = 9/hr.

Now, A worked from
7AM to 10 AM alone before Tap B opened.

Work done in 3
hrs(7-10AM) = 15/hr*3 = 45

Remaining work =
180-45 = 135.

Now, Tap A and B
worked together until Tap C opened at 11AM.

Efficiency of A and
B together = 27/hr.

Work done in 1 hr
(10AM-11AM)= 27.

Remaining Work after
11AM= 108.

Now, all 3 taps are
opened after 11AM

Hence, Efficiency of
A+B+C = 36/hr

Time taken = 108/36
= 3 hrs.

Therefore, 11AM+3hrs
= 14 Hrs= 2PM.

Also can be done in
the following way:-

A opened for (7-11)=
4 hrs.

B opened for (10-11)
= 1 hr

4/12 + 1/15 + 4t/20
= 1.

20+4+12t = 60

12t = 36

== > t=3hrs.

Hence, 3 hrs after
11AM i.e, at 2PM.

4. Two trains
running in opposite directions cross a man standing on platform in 28 sec and
15 sec respectively, and they cross to each other in 22 sec. Find the ratio of
their speed ?

(a) 6:7

(b) 7:6

(c) 4:3

(d) Cannot be determined

(e) None of these

**. (b) 6:7**

__solution:-__
Let Speed of the
train be X and Ym/s

Length of First
train = 28x

Length of Second
train = 15y

Also, (28x + 15y) /
(x+y) = 22

== > 6x-7y = 0

6x = 7y

x/y = 7/6.

5. Three partners A,
B and C invested money in a business in the ratio of 5:3.5 : 5.5 and ratio of
their duration of investment is 2:8/3:1.33. Then what % of total profit will A
get?

(a) 30%

(b) 35%

(c) 37.5%

(d) 40%

(e) None of these

**. (c) 37.5%**

__solution:-__
Money Invested in
the ratio = 5:7/2:11/2 = 10:7:11

The Ratio of
Duration of Investment = 2:8/3:4/3= 6:8:4= 3:4:2

Ratio of their
Profit = 10x3:7x4:11x2 = 30:28:22 = 15:14:11

Profit % of A =
15x100/40 = 37.5%.

6. The ratio of
present ages of son and daughter of a lady is in the ratio of 7:8 and the age
of lady is sum total of ages of her daughter and son. If the ratio of ages of
son after 3 years and the age of daughter 6 years ago is 4 : 3 then what will
be the ratio of the present age of lady and the age of her son after four
years?

(a) 4:5

(b) 5:3

(c) 6:5

(d) 9:5

(e) None of these

**. (d) 9:5**

__solution:-__
Let the present age
of Son and Daughter be 7x and 8x respectively.

Then, Age of Lady =
15x

Now, (7x+3)/(8x-6) =
4/3

== > 21x + 9 =
32x-24

== > 11x = 33 ==
> x= 3

Son’s Age = 21 years

Daughter = 24 years

Lady’s Age = 45
years

Required Ratio =
45/25 = 9/5 = 9:5

7. In a two digit
number the digit at unit's place is less than twice the digit at ten's place by
1. And the difference between the number obtained by interchanging its digits
and the original number is 50% of the number obtained by adding 1 in original
number. What is the original number?

(a) 46

(b) 57

(c) 35

(d) 68

(e) None of these

**. (c) 35**

__solution:-__
Let the number be
10x+y

Now, ATQ, we have
following conditions

(i) y = 2x-1

(ii) 9y-9x =
50%(10x+y+1) = > 9y-9x = 1/2(10x+y+1)

== > 18y-18x =
10x+y+1

== > 17y-28x = 1

Solving (i) and
(ii), we get x=3 and y=5

Thus, Number =
10x3+5 = 35

8. An alloy contains
mixture of two metals A and B in the ratio of 3:5, and the second alloy
contains, mixture of same metals in the ratio of 2.33 : 3. In what ratio should
be both alloy mixed to make a new alloy containing 42(6/7)% metal A?

(a) 1:2

(b) 3:2

(c) 2:3

(d) 1:6

(e) None of these

**. (d) 1:6**

__solution:-__
Quantity of A in
first alloy = 3/8.

Quantity of A in
second Alloy= 7/16.

Let two alloys are
mixed in the ratio x:y

Therefore, % of A in
new mixture = [(3x/8)+(7x/16)]x100 / [x+y]

But, Given % of A in
new mixture = 42(6/7)= (300/7)%

== > [(3x/8)+(7x/16)]x100
/ [x+y] = 300/7

== >
(6x+7y)/16(x+y) = 3/7

== > 42x+49y =
48x+48y

== > 6x = y == > x=y = 1/6

Ratio = x:y= 1:6

9. The profit earned
by a compnay is to be distributed among the managers and officers in the ratio
of 7 : 5. If the number of managers and officers is in the ratio of 7 : 12 the
amount recieved by each officers is 30,000 what was the total profit earned if
the number of managers was 28?

(a) 35 Lakh

(b) 17.5 Lakh

(c) 34.56 Lakh

(d) 19 Lakh

(e) None of these

**. (c) 34.56 Lakh**

__solution:-__
Let the Managers get
Rs.X

7X/12*3000 = 7/5 ==
> X= Rs. 72000

Total Money = 72000*28*12/7
= 34.56 Lakh

10. The profit
earned by a compnay is to be distributed among the managers and officers in the
ratio of 7 : 5. If the number of managers and officers is in the ratio of 7 :
12 the amount recieved by each officers is 30,000 what was the total profit
earned if the number of managers was 28?

(a) 70%

(b) 60%

(c) 65%

(d) 80%

(e) None of these

**. (c) 60%**

__solution:-__
Total Discount Given
= -10-15+150/100 = -25+1.5 = -23.5

Now, Let CP be Rs.
100

SP = Rs. 153

MP =
153x100/(100-23.5)= 153x100/76.5 = 200

Therefore, Marked
Price = 200

On Giving 20%
discount , SP = 200x80/100 = 160.

SP=160

CP=100

Profit = 60%

**Enjoy quiz and don’t forget to impart your precious review.**

**Thanks.**

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