Question

Q9.
Iqbal dealt some cards to Mushtaq and himself from a full pack of playing cards and laid the rest aside. Iqbal then said to Mushtaq "If you give me a certain number of your cards, I will have four times as many cards as you will have. If I give you the same number of cards, I will have thrice as many cards as you will have”. Of the given choices, which could represent the number of cards with Iqbal?
(a) 9
(b) 31
(c) 12
(d) 35​

Answer 1

31

Step-by-step explanation:

Lets assume Iqbal has X number of cards and Mushtaq has Y number of Cards.

Iqbal = X

Mushtaq = Y

Iqbal said to Mushtaq if you give me certain number of cards , Lets assume its be Z number of Cards. then the Equation will be

Iqbal = ( x + z )

Mushtaq = ( y - z )

then Iqbal said I will have four time as many cards as you have. then the equation will be

( x + z ) = 4 ( y - z )  ----------------- eq : 1

x + z = 4y - 4z

x - 4y = -5z ------------ eq : A

After that Iqbal said If I give You the same Number of cards, I will have thrice as many cards as you, then the Equation will be

( x - z ) = 3 ( y + z ) ---------------- eq : 2

x - z = 3y + 3z

x - 3y = 4z  ---------------- eq : B  

Now Minus Eq A from Eq B

x - 4y = -5z

x - 3y = 4z

----------------------

-y = -9z   y = 9z

Now we have the value of y simply putting this value in Eq: B we get

x = 4z + 3(9z)

x = 4z + 27z

x = 31z

Z cannot be more then 1 because if multiplied with 31 it will be 62 which is wrong because playing deck has 52 cards. So value of Z is 1

x = 31 and X is the number of Iqbal's cards.

So Answer 31 is correct.

Answer 2

The number of cards with Iqbal is (b) 31.

Given: If Mushtaq gives Iqbal a certain number of his cards, Iqbal will have four times as many cards as Mushtaq will have.

If Iqbal gives Mushtaq the same number of cards, Iqbal will have thrice as many cards as Mushtaq will have.

To Find: The number of cards with Iqbal

Solution:

Let the number of cards with Iqbal be = p, and

let the number of cards with Mushtaq be = q

Let the number of cards with which transaction occurs be = m

It is said that if Mushtaq gives Iqbal an 'm' number of his cards, Iqbal will have four times as many cards as Mushtaq will have.

∴ Number of cards with Iqbal = p + m

∴ Number of cards with Mushtaq = q - m

Framing the equation according to the condition, we get;

       p + m = 4 ( q - m )

 ⇒   p - 4q = - 5m                                  ..... (1)

It is again said that if Iqbal gives Mushtaq the same number of 'm' cards, Iqbal will have thrice as many cards as Mushtaq will have.

∴ Number of cards with Iqbal = p - m

∴ Number of cards with Mushtaq = q + m

Framing the equation according to the condition, we get;

       p - m = 3 ( q + m )

   ⇒ p - 3q = 4m                                          ..... (2)

Substracting (2) from (1), we get,

       q = 9z                                                    ...... (3)

Putting (3) in (2), we get;

       p = 31z                                                   ....... (4)

Now, it is to be noted that if z > 1 then p = 62, 93, 124,... which is not possible since there are 52 cards in a deck. So, z must be 1.

∴ Putting z = 1 in (4), we get;

      p = 31

Hence, the number of cards with Iqbal is (b) 31.

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