HOT Competition: On Sunday, in Alexa’s stable, the ratio of the number

Sunday -- Ponies: Horses = 4:5.

On Monday, 35 new animals were added (can be ponies, can be horses) and the new ratio Ponies:Horses = 5:8

5:8 = 5+8 = 13. We need the total number of horses on Monday to be a multiple of 13.

I tried reverse calculating using the answer choices.

1. 35 horses on Sunday. Ponies on Sunday = 28. Total = 63. After adding 35 to this, gives us 98, which is not a multiple of 13.

2. Horses = 55. Ponies = 44. Total = 99. Plus 35 = 134. Wrong

3. Horses = 60. Ponies = 48. Total = 108. Plus 35 = 143. which is a multiple of 13.

Correct answer: C : 60.

ANSWER - OPTION C

P:H = 4x:5x
Total animals in stable on Sunday - 9x

Total animals in stable on Monday - 9x+35 = 13y -- (1) (5y+8y = 13y)

So let's start with Option C

H = 60 . This implies X = 12

Equation (1) becomes 143 and hence divisible by 13. Hence we can eliminate Options D & E

Option A & B gives X = 11 & 7 respectively

So the total number of animals on Monday will be 134 & 98, both not divisible by 13 according to equation (1)

Hence , ANSWER - OPTION C

Posted from my mobile device

Solution:
Let animal on Sunday be, 4x+5x (as per ponies and horses ration)
and animal on Monday be, 5y+8y (as per ponies and horses ration), after adding 35 animals,
=> 5y+8y=4x+5x+35
=> 13y = 9x + 35

x and y should be integers as they represent animals, we will go will option to find least value of x and y.

A. 35
=> x = 7 (35/5)
=> 13y = 63+35
=> 13y = 98, y is not integer.

B. 55
=> x = 11 (55/5)
=> 13y = 99+35
=> 13y = 134, y is not integer.

C. 60
=> x = 12 (35/5)
=> 13y = 108+35
=> 13y = 143, y =11.

C is the answer, we need not to calculate further as other values are bigger that 60

D. 65
E. 70

On Sunday, in Alexa’s stable, the ratio of the number of ponies to the number of horses was 4:5. On Monday, she bought 35 more ponies and horses, then the ratio of ponies to horses became 5:8. Assuming that no animal left the stable or died and stable had ponies and horses only, what is the least number of horses that were there in the stable on Sunday?

A. 35
B. 55
C. 60
D. 65
E. 70

Answer should be C.

Let's consider Ponies as P and Horses as H. We know that on Sunday P:H = 4:5. And after adding 35 more ponies and horses on Monday, ratio of P & H changed to P:H= 5:8. Now we have to find out minimum number of Horses on Sunday. Then we have given answer choices.

So sum of number of ponies and horses available on Sunday + 35 should be divisible by 13 ( Ratio P:H on Monday after adding 35 more P & H becomes 5:8)

initial ponies be \(4x\) and initial horses be \(5x\)
let the horses added on monday be \(y\)
\(\frac{(4x+y)}{(5x+35-y)}=\frac{5}{8}\)
by cross multiplication we get
\(32x+8y=25x+175-5y\\
7x+13y=175\\
x=25-\frac{13}{7}y\)
\(y\) can only be \(7\) to give an integer value of x which is mandatory.
so \(x=25-13=12\)
horses are \(12*5=60\)

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