Vaidev had some beads. He gave ²₃ of his beads to Carl and bought 4 new beads. After that, he gave ³₅ of his remaining beads to his sister and bought another 7 new beads. In the end, Vaidev had 33 beads.

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

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

²₅ of his remaining beads = 33 - 7 = 26
¹₅ of his remaining beads = 26 ÷ 2 = 13
³₅ of his remaining beads = 3 x 13 = 39

Number of beads that Vaidev gave to his sister = 39

(b)
⁵₅ of his remaining beads = 5 x 13 = 65

Fraction of his total beads after he gave to Carl
= 1 - ²₃
= ¹₃

¹₃ of his total beads = 65 - 4 = 61
³₃ of his total beads = 3 x 61 = 183

Number of beads that Vaidev had at first = 183 

Answer(s): (a) 39; (b) 183