Question

Dinalal Divides His Property among his four sons after donating RS.20,000 and 10% of his remaining property. The amounts received by the last three sons are in arithmetic progression and the amount received by the fourth son is equal to the total amount donated. The first son receives as his share RS.20,000 more than the share of the second son. The last son received RS.1 lakh less than the eldest son.
10. Find the share of the third son.
option
a) RS.80,000
b) RS.1,00,000
c) RS.1,20,000
d) RS.1,50,000

Answer 1

Answer:

No(8)let d shares are a,b,c,d.

and let property be x.

so d=20000+0.1(x-20000) .. equation 1

now let d differences b/w last three sons be n.

c=d-n

b=d-2n

a=b+20000=d-2n+20000

so a+b+c+2d = x

d-2n+20000+d-2n+d-n+2d = x

5d-5n+20000 = x

putting the value of d from equation 1 we get.

5(20000+0.1(x-20000))-5n+20000 = x

100000+0.5x-10000-5n+20000 = x ... equation 2

as last son received 100000 less than eldest son.

so d-2n+20000 = d+100000

n = -40000 .... equation 3

by putting value of equation 3 in equation 2 we get,

100000+0.5x-10000-5(-40000)+20000 = x

solving this we get x = 620000.

now putting d value of x in equation 1 we get.

d=20000+0.1(620000-20000)

= 20000+0.1(600000) = 80000

therefore c = d-n = 80000-(-40000) = 120000 answer. option (c).