1.3 Marks

The table below shows the age-wise distribution of the population ofReposia. The number of people aged below 35 years is 400 million.

If the ratio of females to males in the ‘below 15 years’ age group is 0.96,then what is the number of females (in millions) in that age group?

[CAT 2000]

1) 82.8

2) 90.8

3) 80.0

4) 90.0

Solution:

Population below 35 years of age = 30 + 17.75 + 17 = 64.75% of the totalpopulation = 400 million

The ratio of females to males in the ‘below 15 years’ age group is 0.96.

i.e. if the total population is 196, then there are 96 females.

Approximately, the number of females (in millions) in the ‘below 15 years’age group

Hence, option 2.

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Section I

2.3 Marks

A student took five papers in an examination, where the full marks werethe same for each paper. His marks in these papers were in theproportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidateobtained 60% of the total marks. Then the number of papers in which hegot more than 50% marks is

[CAT 2001]

1) 2

2) 3

3) 4

4) 5

Solution:Let the maximum marks for each of the paper = 100

∴ Total maximum marks = 5 × 100 = 500

Let the marks obtained by the student be 6x, 7x, 8x, 9x and 10x in each ofthe paper.

∴ 6x + 7x + 8x + 9x + 10x = 60% of 500

40x = 300

∴ x = 7.5

∴ The marks obtained in each of the paper will be 45, 52.5, 60, 67.5 and75.

∴ In 4 papers he got more than 50% marks.

Hence, option 3.

Alternatively

∵ 60% of marks = 8

= 6.67

∴ The score in 4 of the subjects is more than 6.67.

Hence, option 3.

3.3 Marks

A college has raised 75% of the amount it needs for a new building byreceiving an average donation of Rs. 600 from the people alreadysolicited. The people already solicited represent 60% of the people thecollege will ask for donations. If the college is to raise exactly the amountneeded for the new building, what should be the average donation from theremaining people to be solicited?

[CAT 2001]

1) Rs. 300

2) Rs. 250

3) Rs. 400

4) Rs. 500

Solution:

Let the total population be p.

Then the amount already received = 0.6p × 600 = 360p

This is 75% (3/4th) of the amount.

∴ Remaining amount (25%) = (360p)/3 = 120p = 120p

∴ Required contribution per head = (120p)/(0.4p) = Rs. 300

Hence, option 1.

4.3 Marks

Fresh grapes contain 90% water by weight while dry grapes contain 20%water by weight. What is the weight of dry grapes available from 20 kg offresh grapes?

[CAT 2001]

1) 2 kg

2) 2.4 kg

3) 2.5 kg

4) None of these

Solution:Total weight of fresh grapes = 20 kg

In dried grapes, water is 20%.

∴ Grape mass is 80%.

Hence, option 3.

5.3 Marks

The owner of an art shop conducts his business in the following manner: Everyonce in a while he raises his prices by X%, then a while later he reduces all the

new prices by X%. After one such up-down cycle, the price of a paintingdecreased by Rs. 441. After a second up-down cycle the painting was sold forRs. 1,944.81. What was the original price of the painting?

[CAT 2001]

1) Rs. 2,756.25

2) Rs. 2,256.25

3) Rs. 2,500

4) Rs. 2,000

Solution:As the price decreases after the first cycle, it has to decrease after the secondcycle too. Also the decrease in the second cycle will be less than 441 as theoriginal price for the second cycle is less than the original price for the firstcycle.

∴ Price after First Cycle – 1944.81 < 441

Now we consider options.

So, options 2 and 4 are eliminated.

As the percentage change in the price in the first and second cycles is equal,

Only option 1 satisfies this.

Hence, option 1.

Alternatively,

Let the original price of the painting be p.

After the first cycle,

After the second cycle,

∴ (441 + p)2 = 1944.81p

Solving, p = 2756.25

Hence, option 1.6.

3 MarksAt the end of year 1998, Shepard bought nine dozen goats. Henceforth,

every year he added p% of the goats at the beginning of the year and sold

q% of the goats at the end of the year where p > 0 and q > 0. If Shepardhad nine dozen goats at the end of year 2002, after making the sales forthat year, which of the following is true?

[CAT 2003 Leaked Test]

1) p = q

2) p < q

3) p > q

4) p = q/2

Solution:Shepard bought 9 dozen goats at the end of 1998.

Consider that he added 1 dozen goats to it, i.e. 11.11% of 9 dozen.

And he sold 1 dozen to get back the same 9 dozen i.e. 10% of 10 dozen.

∴ He adds 11.11% and subtracts 10% to get the same amount everytime.

∴ p = 11.11% and q = 10%

∴ p > q

Hence, option 3.

Group Question

Answer the following questions based on the information given below.

A certain perfume is available at a duty-free shop at the Bangkok internationalairport. It is priced in the Thai currency Baht but other currencies are alsoacceptable. In particular, the shop accepts Euro and US Dollar at the followingrates of exchange:

US Dollar 1 = 41 Bahts and Euro 1 = 46 Bahts

The perfume is priced at 520 Bahts per bottle. After one bottle is purchased,subsequent bottles are available at a discount of 30%. Three friends S, R andM together purchase three bottles of the perfume, agreeing to share the costequally. R pays 2 Euros. M pays 4 Euros and 27 Thai Bahts and S pays theremaining amount in US Dollars.

[CAT 2003 Leaked Test]

7. How much does R owe to S in Thai Baht?

3 Marks1) 428

2) 416

3) 334

4) 324

Solution:

Price of 1st bottle = 520 Bahts

Price of 2nd and 3rd bottles each = (520 × 0.7) = 364 Bahts

∴ Total cost of all three bottles = 1248 Bahts

Cost per person = 416 Bahts

R pays 2 Euros = 2 × 46 = 92 Bahts

M pays 4 Euros and 27 Bahts = 4 × 46 + 27 = 211 Bahts

S pays the remaining amount = 1248 − (92 + 211) = 945 Bahts

∴ R owes 416 − 92 = 324 Bahts to S.

Hence, option 4.

8.3 Marks

How much does M owe to S in US Dollars?

1) 3

2) 4

3) 5

4) 6

Solution:From the solution to the previous question,

M owes = 416 − 211 = 205 Bahts to S

But, 205 Bahts = 205/41 = 5 US Dollars

Hence, option 3.