# GATE2019-GA-4

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Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs. $150$ more. The cost of the gift was Rs. ____

1. $666$
2. $3000$
3. $6000$
4. $12000$

edited
3
0
6000
0

150*8=1200

1200/2=600 each person

600*10=6000rs

Let us suppose each of the $10$ friends were supposed to contribute Rs $x$.

Hence total cost for gift $= \text{Rs } 10 x$.

Now since $2$ friends won't contribute , hence $8$ friends would have to contribute $(x+150)$ each.

By the sum,

$10x = 8x+1200$

$2x= 1200$

$x= 600$

Hence total cost of the gift $= 10x = \text{Rs. }6000$

edited by
Let the gift net worth is "x".

Therefore, $\frac{x}{10} = \frac{x-(150*8)}{8}$

x = 6000
 Friend Name $A$ $B$ $C$ $D$ $E$ $F$ $G$ $H$ $I$ $J$ ${\color{Blue} {TOTAL\ MONEY}}$ Money Contributed $x$ $x$ $x$ $x$ $x$ $x$ $x$ $x$ $x$ $x$ $10x$

I and J didn't gave the money

 Friend Name $A$ $B$ $C$ $D$ $E$ $F$ $G$ $H$ ${\color{red} {TOTAL\ MONEY}}$ Money Contributed $x+150$ $x+150$ $x+150$ $x+150$ $x+150$ $x+150$ $x+150$ $x+150$ $8(x+150)$

${\color{Blue} {TOTAL\ MONEY}}$ = ${\color{red} {TOTAL\ MONEY}}$

$\Rightarrow\ 10x\ =\ 8(x+150)$

$\Rightarrow\ 10x\ =\ 8x + 1200$

$\Rightarrow\ 2x\ =\ 1200$

$\Rightarrow\ x\ =\ 600$

so , TOTAL MONEY $=10x=6000$

edited by
Suppose each friend share equally cost= x

There are 10 friend so total cost =10x

Two not to decide contribute so  8 friends had to pay 150 more each

8x+150×8=10x

1200=2x

X=600 hence total cost of gift=10×600=6000

Let x be the amount 1 person is contributing and y be the total amount
Now,

10(x) = y _________(1)
2(0) + 8(x+150) = y ___________(2)

8(x) + 1200 = 10(x)
=> 2(x) =1200

x = 600

therefore total amount, y = 10(x) = 6000
let x be the total amount

then per person, they have to give x/10 rs

2 person left

therefore 8*(x/10+150)=x

8*(x+1500)=10*x

8x+12000= 10x

2x=12000

x=6000

X/10=m
X/8=m+150
X=8m+1200
X/10+150=x/8
8x+12000=10x
X=6000

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