Option 1 : 6680
Calculation:
Total number of children in city P = 42000 × 10%
⇒ 4200
Number of girls in city P = 4100 × (3/5)
⇒ 2520
Total number of children in city R = 46800 × 20%
⇒ 9360
Number of girls in city R = 9360 × (4/9)
⇒ 4160
Total number of girls (among the children) in city P and city R together = 2520 + 4160
⇒ 6680
∴ Required answer is 6680.