Vaidev had some marbles. He gave ³₄ of his marbles to Simon and bought 4 new marbles. After that, he gave ³₅ of his remaining marbles to his sister and bought another 7 new marbles. In the end, Vaidev had 23 marbles.

1. How many marbles did Vaidev give to his sister?
2. How many marbles did Vaidev have at first?

(a)
Fraction of  his remaining marbles after he gave to his sister
= 1 - ³₅
= ²₅

²₅ of his remaining marbles = 23 - 7 = 16
¹₅ of his remaining marbles = 16 ÷ 2 = 8
³₅ of his remaining marbles = 3 x 8 = 24

Number of marbles that Vaidev gave to his sister = 24

(b)
⁵₅ of his remaining marbles = 5 x 8 = 40

Fraction of his total marbles after he gave to Simon
= 1 - ³₄
= ¹₄

¹₄ of his total marbles = 40 - 4 = 36
⁴₄ of his total marbles = 4 x 36 = 144

Number of marbles that Vaidev had at first = 144 

Answer(s): (a) 24; (b) 144