Three Thieves – DI Set For CAT 2018-2019 students

Three thieves are reporting their shares in the 2000 gold and silver coins looted. The ratio of gold to silver coins is 2:3. The following table shows the percentage distribution of coins with each thief.

1 Based on the above information, which of the following is true?

(a) x = y

(b) x < y

(c) x > y

(d) Data Insufficient

Sol.  b)

Since the overall percentage of gold coins in the loot is 40% and for both Shamu and Gopi the gold coins account for 60% of their share of coins, thus we can deduce that x<40% (for the average of the gold coin tally to be 40%).

Similarly, overall percentage of silver coins in the loot is 60% and for both Shamu and Gopi the silver coins account for 40% of their share of coins, thus we can deduce that y>60%.

Hence x<y

2 If the number of coins with Ramu is 800, then what is the value of 3y + 2x?

(a) 135

(b) 290

(c) 225

(d) Data Insufficient

Sol. b)

All coins with Ramu would be categorized in one of the two categories, gold or silver, thus x+y = 100

So the expression 3y + 2x = 3(x+y) –x = 300-x

Now, if Total number of coins with Ramu is 800, the coins with Shamu and Gopi combined is 1200.

60% of coins with Shamu and Gopi are Gold coins, thus Ramu’s share of gold coins becomes (2000*2/5) – (.6*1200) which is also equal to x% of 400

Or x*800/100=800-720

Or x = 10%

And the value of expression 3y + 2x = 3(x+y) –x = 300-x = 300-20 =290

3 If the ratio of the number of coins with Gopi : Shamu : Ramu is 2:3:5 what is the ratio of the number of gold coins with them?

(a) 18 :27 :15

(b) 6 :9 :15

(c) 8 : 23 : 8

(d) None of these

Sol. a)

Refer to the table below

The final ration 6:9:5 is equal to 18:27:15