Question

1 24. Nitya and Satya have some marbles with them. Nitya
says to Satya, If you give one marble to me, we will
have equal number of marbles'. Satya says to Nitya
If you give me one marble, I will have twice the nu
ber of marbles you have'. How many marbles do
and Satya have respectively?
(A) 4,6
(B) 5,7
(C) 6,4
(D) 7,5

Answer 1

Answer:

$\large{\underline{\boxed{\mathfrak\blue{ \: \: \: Answer :- \: B)5,7 \: \: \: }}}}$

Given:-

1st case:-

• If Satya gives 1 marble to Nitya,then number of marbles of Satya = Number of marbles of Nitya.

2nd case:-

• If Nitya gives 1 marble to Satya, Number of marbles of Satya = 2 × Number of marbles of Nitya.

To find:-

• Number of marbles of Satya & Nitya

Solution:-

Let the number of marbles of Satya and Nitya be x & y respectively.

A/Q,

At first,

$\dashrightarrow\sf (x - 1) = (y + 1) \\\\\dashrightarrow\sf x - 1 = y + 1 \\\\\dashrightarrow\sf x = y + 1 + 1 \\\\\dashrightarrow\sf\green{x = y + 2 \dots \dots \dots (eq.1)}$

Secondly,

$\dashrightarrow\sf 2(y - 1) = (x + 1)\\\\\dashrightarrow\sf 2y - 2 = x + 1 \\\\\dashrightarrow\sf x + 1 + 2 = 2y \\\\\dashrightarrow\sf x + 3 = 2y \\\\\scriptsize\sf{\: \: \: \dag \: \: (Putting \: values \: from \: (eq.1)}\\\\\dashrightarrow\sf y + 2 + 3 = 2y \\\\\dashrightarrow\sf y + 5 = 2y \\\\\dashrightarrow\sf 2y - y = 5 \\\\\dashrightarrow\large{\underline{\boxed{\sf\blue{y = 5 }}}}$

$\rule{100}{1}$

• Putting value of y in (eq.1) :-

$\dashrightarrow\sf x = 5 + 2 \\\\\dashrightarrow\large{\underline{\boxed{\sf\green{x = 7 }}}}$

$\rule{200}{1}$

• Marbles of Satya and Nitya :-

$\dashrightarrow\sf Marbles \: of \: Satya = \large{\boxed{\sf\blue{7 }}}$

$\dashrightarrow\sf Marbles \: of\: Nitya = \large{\boxed{\sf\green{5 }}}$

Answer 2

Given :

• If Satya gave one marble to Nitya then they both will have equal no. of marbles. (First Case)

• If Nitya gave one marble to Satya then Satya will have twice the no. of marbles Nitya have. (Second Case)

To Find :

• How many marbles do Nitya and Satya have.

Solution :

Let the no. of marbles Nitya have be x and no.of marbles Satya have be y

_________________________

$\dag \: \sf \green{ Equation \: formed \: of \: First \: Case :}$

$\sf \longrightarrow \: x + 1 = y - 1$

$\sf \longrightarrow x - y = - 1 - 1$

$\sf \longrightarrow x - y = - 2...(i)$

$\dag \: \sf \green{ Equation \: formed \: of \: Second \: Case :}$

$\sf \longrightarrow \: y + 1 = 2(x - 1)$

$\sf \longrightarrow \: y + 1 = 2x - 2$

$\sf \longrightarrow \: y - 2x = - 2 - 1$

$\sf \longrightarrow \: y - 2x = - 3.$

$\sf \longrightarrow \: 2x - y = 3$

$\dag \: \sf \: \green{Solving \: Equation \: i) \: and \: ii) : }$

$\longrightarrow\sf \: x - y = - 2 \\ \: \: \: \: \: \: \: \: \sf \: 2x - y = 3$

$\sf \longrightarrow \: x - 2x + y - y = - 2 - 3$

$\sf \longrightarrow \: - x = - 5$

$\sf \longrightarrow \red{ x = 5}$

$\dag \: \sf \: \green{Putting\: the\: value\: of\: x\: = \: 5\: in\: equation\: i) }$

$\sf \longrightarrow x - y = - 2$

$\sf \longrightarrow 5 - y = - 2$

$\sf \longrightarrow - y = - 2 - 5$

$\sf \longrightarrow - y = - 7$

$\sf \longrightarrow \red{ y= 7}$

Hence,Nitya has 5 marbles and Satya has 7 marbles.