Exam Corner

# Solved Math’s Questions from GSA Past Papers of CSS 2020 | CSS 2019 | CSS 2018

Contents

## GSA CSS 2020

Blood Groups of inhabitants of a village were checked. It was found that 600 people possessed blood group A, 650 possessed blood group B, 550 had blood group AB and 200 have blood group O.

(i)                 Calculate the probability of having blood group B.

(ii)               Calculate the probability of having blood group O.

SOLUTION:

Blood Group A = 600

Blood Group B = 650

Blood Group AB = 550

Blood Group O = 200

Total Number = 2000

Probability = n(blood group)/total number

Thus;

Probability of B = 650/2000 = 0.325

Similarly,

Probability of O = 200/2000 = 0.1

A group of 50 men can construct 20 kilometer road in 40 days. How long will 70 men take to complete same length of road?

Solution:

Men                      Days

50                             40

70                             x

Thus:

x/40 = 50/70

x = 2000/70 = 28.57

Hence, 70 men will take 28.57 days.

Zahid left a property worth Rs 1750,000/. His family had to pay off a debt of Rs 150,000/. The rest of money was distributed between a son and a daughter. How much did each child receive if share of a son was double than that of a daughter?

Solution:

Property left by Zahid = 1750,000

Debt      = 150,000

Remaining Amount = 1600,000

Dividing the remaining amount by 3 = 1600,000/3 = 533,333.333

As son’s share is double, so:

Son’s share = 2(533,333.333) = 1066,666.67

Daughter’s share = 533,333.333

Tariq can do a tailoring job in 6 hours. Sajid does the same job in 4 hours. Irfan does it in 8 hours. Tariq and Sajid start doing the work. Sajid leaves after two hours and Irfan replaces him. How long would it take to complete the work?

Solution:

Tariq does job = 6 hours

Sajid does job = 4 hrs

Irfan does job = 8 hrs

Together, Tariq and Sajid do job in;

1/t = 1/6 + ¼

1/t = 5/12

T = 12/5 = 2.4 hrs

Together, Tariq and Irfan do job in;

1/t = 1/6 + 1/8

1/t = 7/24

T = 24/7 = 3.42 hrs

Work completed by Tariq & Sajid in two hours;

= 100 * 2/2.4

= 83.33 %

The remaining work is = 100 – 83.33 = 16.66 %

Time taken by Tariq and Irfan to complete the remaining work will be;

= 3.42 * 16.66/100

= 0.569

Hence, the total time taken in completing the work is;

2 + 0.569 = 2.569 hrs

## GSA CSS 2019

Moiz was trying to sleep at one night but there was too much noise around him. His clock ticked every 5 second; a tap was dipping every 7 second and a pet dog snored every 12 second. He noticed on his clock that all three things happened together on the stroke of mid night. Find after how many seconds all three things happened together again?

Solution:

Clocked ticked every 5 sec.

Tap dipped every 7 sec.

Dog snored every 12 sec.

To find out the second when all three things happened together, simply take L.C.M

By taking L.C.M of 5, 7, 12, we will get 420.

Thus, all three things happened together after 420 seconds.

The cost for hiring a car for 2 days in 2018 was Rs 264 which was 20% more than in 2013. What was the cost for hiring a car for 2 days in 2013?

Solution:

Let the cost in 2013 = x

As given in 2018;

X + 20%(x) = 264

X + 20x/100 = 264

120x/100= 264

X = 26400/120

X = 220

Thus, in 2013, the cost for hiring a car for two days was Rs 220.

Moiz and Mair share a lottery win of Rs 2000 in the ratio 1:4. Moiz then share his part between himself, his wife and their son in the ratio 4:5:1. How much more does his wife get over their son?

Solution:

Amount = 2000

Ratio  1 : 4

(Sum 1 + 4= 5)

Moiz’ share is 2000*1/5 = 400 rupees.

Now,  the distribution ratio among himself, wife and son is;

4 : 5 : 1

(sum = 10)

Share of wife = 400*5/10 = 200 rupees.

Similarly, share of son = 400*1/10 = 40 rupees.

Thus,

200 – 40 = 160 rupees.

Hence, Moiz’ wife gets 160 rupees more than their son.

A farmer keeps hens and rabbits on his farm. One day, he counted a total of 70 heads and 196 legs. How many more hens than rabbits does he have?

Solution:

Let hens be ‘x’ & rabbits be ‘y’

As given;

1x + 1y = 70         – (i)         (for heads)

2x + 4y = 196      – (ii)        (for legs)

Multiplying equation (i) by 2, we get

2x + 2y = 140      – (iii)

By subtracting eq (iii) from (ii), we will get

2y = 56

y = 28                    (thus, there are 28 rabbits)

Putting y =28 in eq (i)

x + 28 = 70

x = 70 – 28

x = 42                    (hens are 42)

Thus, the farmer has 14 more hens than rabbits.

Each packet of washing powder carries a token and 4 tokens can be exchanged for free packet. How many free packets will I receive if I buy 64 packets?

Solution:

64 packets = 64 tokens

64/4 = 16 Free Packets

Moreover, 16/4 = 4 More Free Packets

Yet, 4/4 = 1 More Free Packet

Adding all the free packets, we get;

16 + 4 + 1 = 21 Free Packets

## GSA CSS 2018

It takes 3 liters of paint to cover an area of 24 square meters. What percentage increase in the quantity of paint would be required to cover an area of 50.4 square meters?

Solution:

3 liters of paint covers 24 square meters

Hence,  1 liter of paint would cover = 24/3 = 8 square meters

So, the paint required to cover an area of 50.4 square meters would be;

50.4/8 = 6.3 liters

Increase in paint = 6.3 – 3 = 3.3 liters

In order to find out the percentage increase;

100*increase/original value = 100*3.3/3 = 110 %

Tahir started a business with a capital of Rs 15,000. After 5 months Umar also joined him with an investment of Rs 30,000. At the start of 9th month, Usman joined them by investing Rs 45,000. At the end of the year they earned a profit of Rs 406,000. Find the share of each one.

Solution:

For finding investments, we would multiply capital and months respectively.

Tahir invested 15000 for 12 months.

So, 15000*12 = 180000

Umar invested 30,000 for 7 months.

So, 30,000*7 =210000

Usman invested 45000 for 4 months.

So, 45000*4 = 180000

Now, we will find ratio to divide profit.

Ratio of their investments is;

180000 : 210000 : 180000

18 : 21 : 18

6 : 7 : 6

Sum of ratios = 6 + 7 + 6 = 19

Total earned profit is = 406000

Tahir’s share = 406000*6/19 = 128210.5

Umar’s share = 406000*7/19 = 149579

Usman’s share = 406000*6/19 = 128210.5

A man left his property of Rs 640,000. A debt of 40,000 was due to him and Rs 5,000 was spent on his burial. Distribute the amount between his widow, one daughter and two sons according to the Islamic law.

Solution:

Man left = 640000

Debt amount = 40000

Amount spent on burial = 5000

Net Amount;

640000 – 40000 – 5000 = 595000

Now, widow’s share is 1/8 according to Islamic law.

Hence, 595000*1/8 = 74375 rupees

Remaining amount is, 595000 – 74375 = 520625

As per Islamic law, the daughter’s share is equal to half of the son’s share.

son : son : daughter

2 : 2 : 1

(sum of ratio = 5)

Hence, each son’s share:

520625*2/5 = 208250 rupees.

And, daughter’s share is;

520625*1/5 = 104125 rupees.

Verification:

widow’s share + son’s share + son’s share + daughter’s share = total amount left

74375 + 208250 + 208250 + 104125 = 595000 